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The paper explores the use of shadows in the very design of Classical Greek temples. It also analyzes the role of cast-off and carry-on shadows in the Temples' morphology by utilizing the author's General Dynamical Theory of Shadows. Further, the paper produces a comparative analysis of five Classical Greek Temples. It also supplies an new angle to the Parthenon Marbles' inappropriate housing in Museums
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Moving Shadows and the Temples of
Classical Greece
Dimitrios S. Dendrinos
Emeritus Professor, School of Architecture and Urban Design, University of
Kansas, Lawrence, Kansas, USA.
In Residence at Ormond Beach, Florida, USA.
April 10, 2017
Relief, part of the Pan-atheniac Procession at the Parthenon’s Western Frieze:
section II 2. British Museum.
Table of Contents
Brief literature review
The goldilocks bandwidth of shadows in the Temperate zone
Use of Shadows: was it the Pinnacle of Classical Greek Architecture?
Shadows and Classical Greek Temples
Introduction, origins
A Renaissance example: aftermath
Five Classical Greek Temples
The Temple of Hera (Temple E) at Selinunte
The two Hera Temples at Paestum
The Parthenon
The Temple of Epicurius Apollo at Bassae
Comparative statistical analysis
Data: vital statistics and key ratios
Initial and preliminary findings
The reliefs of Classical Greek Temples and the Parthenon Marbles
General observations
A Note on the Parthenon Marbles
Conclusions and Suggestions for Further Research
Appendix: More Photos and Analysis of the Five Temples with their Shadows
Legal Notice on Copyright
The Parthenon on the Athens Acropolis, aerial view from the Northwest
The paper constitutes a preliminary attempt to analyze the role shadows played in the design of
Classical Greek Temples. To set the foundations of this rather neglected subject in the extensive
literature on Greek Temples, vital statistics are obtained and key ratios are derived from five
selected Greek Temples constructed in the period covering the middle of the 6th Century BC to
the middle of the 5th Century BC. Detailed analysis follows pinpointing the effect cast-off and
carry-on type shadows had on the Temples’ design. This analysis focuses on the Sun-induced,
sharp in their borders shadows, cast by the Temples’ peristyle columns, as well as by the various
components of their entablature. Emphasis is placed in examining the specific impact of cast-off
shadows on the characteristic of entasis built into the Temples’ superstructure. In addition, the
accentuating role that carry-on shadows played in the friezes’ reliefs and the sculptures of their
pediments’ tympana is displayed. How movement, implanted by the reliefs and sculptures’
makers, is affected by their carry-on shadows is extensively discussed. Within this context, a Note
is offered on the Parthenon Marbles currently housed in the British Museum. Comparative
analysis is carried out, which shows that, although each Temple had its own fingerprint in its
structural components’ measurements, some aggregate statistics can be derived which are
meaningful in classifying Classical Greek Temples. Suggestions for further research are supplied.
Brief literature review
In a previous set of papers, see [1.1], [1.2], [1.3] the author analyzed the physical nature proper
of Sun-induced cast-off and carry-on shadows. The papers elaborated on the spatial (over
different latitudes) and temporal (over the different hours of a day under sunlight, and over the
365 days of a year) macro-dynamics as well as the micro-dynamics (over very small time spans)
of shadows. In [1.1] and [1.3] the case of shadows with sharply delineated borders was analyzed.
Whereas in reference [1.2] the fuzzy nature of shadows was addressed. The ensuing uncertainty
regarding the shadows’ lengths and widths and their micro-dynamics was pointed out, and
methods on how to approach the inherent fuzziness in shadows cast by an object were outlined.
Furthermore, in a set of papers (see [1.4], [1.5], [1.6]), the role of shadows in certain Neolithic
monuments was exposed, both to the extent that these monuments’ cast-off shadows under
sunlight shaped the designed morphology of these monuments, and also with regards to the
possible role shadows played in their symbolic and ceremonial functions. In [1.4], the case of the
shadows cast off by the pillars in structures C and D, Layer III of Gobekli Tepe was presented, as
shadows cast by each pillar would touch the other at sunrise and sunset during each day of the
year. In [1.5], the case was discussed of shadows determining the distances between stones, as
well as the distances among the various arced (and not straight lines forming - as erroneously
presented in the literature) strings of stones, at Le Grand Menec monument at Carnac in Brittany.
Finally, the role of shadows in determining the spacing of the quasi-elliptical (and not “horseshoe-
shaped”, as routinely is reported in the literature) Trilithons Ensemble of sarsens at Stonehenge
Phase 3 II was shown in reference [1.6]. It was found that the distance between the outer ring of
the 30 standing sarsens and the ten standing Trilithons quasi-elliptical arc was the length of a
Sun-induced shadow cast off by the southernmost sarsen at the outer circular ring of stones at
noontime during Equinox. Other orientations embedded into Stonehenge Phase 3 II were also
uncovered, and the role of shadows in them was extensively discussed in [1.6].
Collectively, the aforementioned papers presented a General Dynamical Theory of Shadows, and
a number of features from that theory were expanded in them, with specific empirical evidence
drawn from three cases involving Neolithic monuments. Much of all that will not be repeated
here. The subject of shadows and its connection to monuments has a relatively recent history.
This brief history is expanded in the work by David Smyth, see reference [2.1]. For more on the
existing literature see the references in both [1.1] and [1.6]. Notable is also in this literature the
work by G. T. Meaden, see for example [2.2]. An on-going discussion on these issues is taking
place in [2.3].
Studying shadows, potentially, could supply a strong linkage between monuments over the
millennia, thus illuminate the analysis of these monuments’ evolving architectonic lineage from
the Neolithic to the Era of Classical Greece down to their Renaissance architectonic aftermath.
The goldilocks bandwidth of shadows in the Temperate zone
The extended analysis of papers [1.1] – [1.6], especially reference [1.3], makes clear that below
the Tropic of Cancer and above the 60 in latitude on the Earth’s Northern Hemisphere cast-off
shadows are not particularly conducive to architectonic exploitation, being perennially and for
extended time periods in the course of a day either too short or too long. However, shadow
conditions are different in latitudes between these limits in Western Eurasia and Northern Africa.
These latitudes contain sites such as Abu Simbel (at about 2220’13”N) to the South, and
Meashowe (at about 5859’48”N) to the North, that are hallmarks in monumental Architecture.
At these latitudes, conditions prevail which allow for a broad enough variation in Sun-induced,
cast-off shadows’ lengths during the day (or Moon-induced night shadows), over the course of a
year, permitting meaningful and informative inclusion of their effects upon the design of
monumental and ceremonial structures. The bandwidth between the Tropic of Cancer and the
60 latitude constitutes within the Temperate zone an environment suitable for the design
exploitation of shadows in monumental construction, forming a “shadows goldilocks zone”.
Within that latitude, and in fact almost halfway between the two possible extremes, where
shadows are architecturally exploitable, one finds some stellar examples of Classical Greek
Temples (CGTs). Among them is the Temple of Hera (or of Aphrodite, and in any case, what has
been designated as “Temple E”) at Selinunte (at about 3734’59”N), a circa middle 6th century BC
structure in Sicily; the First (circa 550 BC) and Second (circa 470 BC) dedicated to Hera Temples
at Paestum (both located at about 4025’20”N) in the Apennine Peninsula; the Parthenon (at
about 3758’18”N), designed by architects Kallikratis and Iktinos; and the Temple of Epicurius
Apollo (at about 3725’47”N), its design generally attributed to Iktinos. Both are middle of the 5th
Century BC Temples, on the Greek Peninsula.
A number of other CGTs can be mentioned of course, falling within this goldilocks bandwidth,
and by including them one could carry out a more extended comparative analysis. But these five
Temples will be enough to initially make the points that need be made. Incorporating more
Temples and obtaining a random sample from them could potentially and quite fruitfully expand
the present analysis – a task left to future research. To the author’s knowledge, not much has
been written (or said) about the role shadows cast in CGTs, or on the manner in which both cast-
off and carry-on types of shadow effects have been captured by and incorporated into their very
design. Similarly, not much has been written about a comparative analysis of CGTs, along the
lines reported here, covering both their vital statistics and important rations characterizing them.
Hence, the material to be discussed in the next sections constitutes to a large extent novel
propositions and suggestions, to the author’s knowledge. Points made regarding the specific role
shadows played at a particular Temple will not be repeated for the rest. In each case, different
topics with respect to shadows’ use will be elaborated, specific to each case – although most are
shared by all five, and in fact they are shared by all Greek Temples and beyond them by other
Greek edifices as well.
Use of Shadows: was it the Pinnacle in Classical Greek Architecture?
Greek Temples didn’t appear in a vacuum. And shadows didn’t start playing a role with Classical
Greek Temples. The lineage of religious and ceremonial monuments goes far back well into the
Neolithic, and so do the shadows and their effects on them. By the time CGTs were erected
however, the role of shadows in monuments and the role proper of monuments themselves had
been largely transformed. Their Astronomy-related utilization (i.e., their capacity to act as
observatories, calendars and clocks), the use, symbolism and ceremony related functions
embedded onto and associated with Neolithic monuments, over the ensuing millennia evolved.
By the Era of Classical Greece, the monumental lineage’s morphology and the associated socio-
cultural use of monuments were transformed. Monuments became a means to display a deeper
and more sophisticated astronomical and mathematical knowledge, born by innovations in the
monuments’ structural design and complexity. CGTs became a means of exhibiting a new
understanding of the Universe, and a far more complex socio-cultural reality and milieu than
those captured by Neolithic monuments. Monuments manifested a different content in both
their meaning and functions. From an exclusively utilitarian exploitation of a monument in the
Neolithic, to more of a monument with an aesthetic appeal in Classical Greece
Within this context, the roles shadows played in these monuments was also transformed. The
structural complexity of monuments (and in specific CGTs) reached extraordinary levels of
sophistication, partly manifested in their embedded multiple manifestations of entasis, a topic
which will be extensively addressed in this paper, especially how shadows are related to it.
Shadow macro-dynamics, exhibited over the course of a day (under either sunlight or moonlight)
and over the course of a year, acquired a role enhancing the visual effect of their presence, rather
than their merely instrumentation and Metrology related use, for the acquisition of astronomical
information. In Classical Greek monuments, the astronomical information already acquired was
embedded in them; whereas, in Neolithic monuments, it was acquired, to the extent that it did.
This evolution was achieved by adding and building onto CGTs the prior experiences and
knowledge cumulatively obtained since the Neolithic, where the roots of many features
encounter later in CGTs were first laid out and can be found. By incorporating the monuments’
cast-off shadows effects on their surroundings in the overall design, site plan and Temple
orientation the architects of the CGTs followed in part the Neolithic architect, albeit for different
and far more socially complex and aesthetically pleasing reasons. Adding onto the prior
achievements of monumental Architecture, and by designing a far more morphologically,
functionally and spatially complicated monument, where much attention was paid to the
numerous and various intricately detailed architectonic structural and decorative features, the
architect of CGTs incorporated a complex dynamic interplay of shadows into the Temple’s design.
That dramatic, theatrical in essence, choreographic interplay of shadows with elements of the
built structures and sculpted surfaces reached unprecedented levels of sophistication.
A number of CGTs’ features will be analyzed in this paper, where that choreographic interplay is
shown to be in full swing. For example, the columns of the Temples’ peristyle will be shown to
cast off a complex array of shadows upon the cella and the surrounding ground. The exquisitely
carved flutes of the Temples’ peristyle column shafts, and the artfully varying depths of the
complex in design entablature reliefs and sculptures presented opportunities to the CGT’s
architect to utilize carry-on shadows’ effects upon the Temple’s architectonic design, in a manner
enhancing the aesthetic appeal of their sculpted detail with their ability to convey a sense of
eternal, as well as periodic, motion.
Changing shadows would add to actually immobile structures a sense of mobility, beyond the
intended illusionary sense of motion potentially implanted through the iconography of the
sculptures. In effect, shadows’ dynamics would enhance an illusion of transient and ephemeral
mobility. Motion became a hallmark characteristic of the structural components in Classical
Greek Architecture. Incorporating periodic and regular change through shadow dynamics,
emanating from the detailed features of columns and reliefs, a sense of theatrical performance
was implanted into CGTs. It was an ingenious way to grant life to otherwise inanimate objects.
Possibly, this was the pinnacle attained by Classical Greek Architecture.
Marble relief from the frieze of the Temple of Epicurius Apollo at Bassae; Lapiths fighting
Centaurs: an example of carry-on shadows effects. British Museum. Source of photo: [2.22].
Shadows in Classical Greek Temples
Introductory comments
At the outset, it must be noted that shadows and their effects were by no means the sole factor
(or even the most critical of factors) that shaped Classical Greek Temples of a Doric style, the
style of the five Temples to be reviewed in this paper. But it was a major factor. It would be as
absurd to argue that it was the main factor as it would be to argue that it was not a major one.
Shadows certainly played a critical role in the Temples’ morphology and design specifications, as
empirical evidence and comparative analysis to be supplied here will show, as a first effort. It is
upon this part of the paper the task to record and evaluate the extent to which both cast-off and
carry-on shadows played a major role in shaping the site and floor plans of these Doric (and other
style, Greek) Temples, as well as their frontal and side views (elevations) and cross sections.
Many elements of CGTs can be singled out for examination under the either cast-off and/or carry-
on shadows lens. For simplicity, in the following sections, only the major components (and in
their totality, rather than their detailed composition) of CGTs will be examined, as to their cast-
off shadow effects. Attention will center on their peristyle’s columns, their entablature, and the
outer walls of their cella (a space which includes the pro-naos, naos and adyton – the area
designated for the safe keeping of the Temple’s valuables and sacred items and furnishings). In
these sections, more detailed focus will be placed onto the individual columns of the Temples’
peristyles cast off shadows on the cella’s exterior walls, and the shadows cast off from the
entablature’s architrave onto the Temples’ columns. Whereas, in the final section, the focus will
be on CGTs entablatures’ reliefs (those on the friezes’ metopes and the pediments’ tympanum),
for the five Temples selected for comparative analysis. These reliefs and sculptures’ carry-on
shadows will be scrutinized, and a special reference to the Parthenon Marbles will be made.
Although the main subject of this study isn’t the exploration of CGTs’ either deep architectural
origins and roots, which span more than two millennia and come from vast and culturally diverse
spaces in Western Eurasia and Northern Africa (touching monuments of the Neolithic and the
Bronze Age); or their considerable impacts and influences reaching through the Roman,
Byzantine, and Medieval religious monuments and other socio-cultural structures down to the
Renaissance and Modern Architectures; some limited elaboration will be offered along these
lines. The examples selected are intended to supply arguments indicative of a strong and evolving
architectonic lineage in Temple design. These examples are also intended to expose some novel
aspects, within a research endeavor, towards pinpointing and more firmly establishing the
intricate and complex (morphologically and culturally) connections linking spaces of worship and
religion over the millennia, and the role shadows played in them.
All Temples contain an inner sanctum and a designed space often (although not always)
surrounding it, forming and acting as an intermediate space between the sacred space and the
outside environment. This is an architectonic feature going back to Neolithic religious
monuments. In the case of Stonehenge, for example, the outer ring of the 30 standing sarsens
and their 30 lintels create an intermediate space before the space formed by the ten sarsens with
their five lintels is reached. One may argue that the Trilithons ensemble is the inner sanctum of
Stonehenge, the equivalent space and maybe origin of the cella in CGTs. Some evidence involving
shadows will be shown in this paper, backing up this proposition. It shows that the way shadows
affected Stonehenge 3 II design, it similarly affected the design of the Temple of Epicurius Apollo.
Next, some exposition of the Doric CGTs’ roots will be shown. In part, new evidence will be
presented that relates to the Doric columns, a part of the Doric CGTs superstructure which will
attract the brunt of this paper’s analysis. This evidentiary finding is somewhat unexpected and it
involves Middle (XI – XII) Dynastic Egypt tombs. Following that evidence, subsequently, the
extraordinary effect shadows played in Neoclassical Architecture will be highlighted. Classical
Greek Temples had significant architectural influences, inter-temporally (spanning more than
two millennia) and inter-spatially (over a number of Continents). From all those examples, the
case of a Renaissance Architecture (early 19th century) German Castle will be presented. It clearly
demonstrates the manner in which the shadows’ effects were incorporated into the structure’s
design. The impressive shadows, generated by the edifice’s design, are majestically displayed in
all sides of the structure, at different hours of a day, and at different times of the year.
Origins of the Doric Temple
It is generally considered that the (archaic and classical) Greek Temples’ architectonic roots are
found in the Mycenaean of the 14th century BC Megaron (ΜΕΓΑΡΟΝ), a rectangular masonry
structure with wooden columns in it. Mycenaean monumental structures were preceded by the
19th century BC Minoan Palace multi-story edifices, comprising masonry construction with
wooden columns as well. However, deeper roots than that (which also include their Astronomical
forebears, in so far as astronomical alignments are concerned) can be sought in both the
rectangular sandstone Temples of Uruk V Eanna District (circa 3400 – 3100 BC) in Lower
Mesopotamia (at 3119’20”N), and in the Egyptian early Dynastic Monumental Architecture.
Two important cases will be very briefly reviewed here, both from Ancient Egypt. One involves
the earliest use of a column; it is encountered in the large scale Temple complex of Karnak (at
2543’07”N) at Luxor, in the region of Thebes; the other (and surprising) root concerns the Doric
order in columns: the bed-rock carved stone columns of the (VI, XI, XII Dynastic Egypt) Beni Hasan
tombs at el-Minya (at 2807’10”N) near present day Cairo.
Although the site at Karnac involved Temples since the eleventh dynasty of the Middle Kingdom
(circa the 22nd till the 20th century BC), it was the work carried out by Pharaohs of the 18th Dynasty
that will be briefly visited as being of relevance here. The Temple of reference is the Great
Hypostyle Hall, which at its initial phases sported massive columns in lotus form made out of
cedar. They were commissioned by Pharaoh Thutmose I; he reigned in the period circa 1526
1513 BC.
However, these wooden pillars were replaced later by equally massive masonry (sandstone)
pillars, to a limited extent by Thutmose I himself. Most of the wood to stone transition though
was undertaken by Thutmose III (he reigned in the period ca 1479 to 1425 BC) and to an extent
by Hatshepsut (she co-reigned with Thutmose III during her reign in the ca 1478 to 1458 BC
period). Of note (in the discussion on shadows and sundials, and the possible use of menhirs,
pillars, orthostats, obelisks and columns as timers and specific forms of gnomons in the Neolithic
and Bronze Age, see the issue addressed more extensively in [1.4]) is the obelisk (which is still
standing), one of the oldest obelisks in Egypt – that by Thutmose I – inside the Karnak complex.
He commissioned two obelisks in fact; however, the second one has collapsed.
It is also noted, that the orientation of the Great Hypostyle Hall is towards the Winter Solstice
sunrise, and the Summer Solstice sunset. One may feel confident that the origins of Temples with
colonnades can be safely attributed to the Karnak complex of Temples in Dynastic Egypt.
Figure A.1. Beni Hasan tomb of Amenemhet (XII Dynasty) interior columns, carved off the
sandstone bedrock. The columns exhibit a very strong structural and morphological resemblance
in their shaft and capital to the Doric order. Public domain photo.
The second case we shall briefly review is the East Nile riverbank (with a West facing entrance)
bedrock carved tombs at el-Minya, currently going by the name of “Beni Hasan” tombs, see [2.8].
There are about 40 of these, mostly non-royal social elite, tombs that have been excavated so
far. A few tombs go back to the VI dynasty, although most are XI and XII dynasty tombs (ca 20th
and 19th century BC). Of special interest here, is the fact that some of these tombs’ (both exterior
and interior) columns, carved directly out of the sandstone bedrock, bear strong resemblance to
the austere Doric column order, see Figures A.1, and A.2.
Figure A.2. Beni Hasan exterior tomb exterior columns, carved off the sandstone bedrock.
Noticeable is the non-protruding abacus of the column. Public domain photo.
Both cases, the interior columns shown in Figure A.1 and the exterior tomb columns shown in
Figure A.2, show a Doric shaped austere column order with a square abacus supporting the
epistyle (architrave or ΕΠΙΣΤΥΛΙΟΝ), although they do not have the convex echinus (the part of
the capital between the shaft and the abacus) which Doric order columns do. This concludes the
very brief History of the origins and roots, both short (Mycenaean and Minoan) and long
(Mesopotamian and Egyptian), of CGTs. Before we elaborate on the five selected Classical Greek
monuments, as our empirical evidence case studies to validate the proposition that shadows did
play a major role in their design, another case of a far more recent monumental structure will be
presented. Hopefully, it will drive home the import of shadows in classical architectonic design.
A Renaissance example: aftermath
Since most of the CGTs no longer exist with their entire structure in place, thus hindering one
from fully appreciating the extent to which shadows complemented their built (and completed)
ensemble, examples of contemporary edifices that have been heavily influenced by CGT’s
Architecture (or more precisely by Roman Architecture, which in turn in its morphology almost
entirely and faithfully copied Classical Greek monumental Architecture) offer a glimpse into the
CGT’s views with shadows in the Temperate zone. In Figures B.1, B.2 and B.3 the case of a 19th
century Renaissance Castle, the Belvedere on the Pfingstburg, Germany (at 5225’08”N) is
shown. Its frontal Southeastern view is in Figure B.1; one of its pair of colonnades is in Figure B.2;
and its site location is in Figure B.3.
The striking cast-off shadows effect of the Grand Entrance to the Castle and the composition of
its two flanking Wings (crowned by a pair of colonnades) in the design of the Castle’s
Southeastern façade, facing the Winter Solstice sunrise, is shown in Figure B.1.
Noticeable is the intentional design of the façade to accommodate the shadows’ angle at the
righthand side (in the case shown, close to 3pm local time). The symmetry attained by
incorporating the shadows within the architectonic detail of the Castle’s structure is indeed
remarkable. Similarly, remarkable is the cast-off shadows’ effect of the two Wings’ colonnades.
The columns’ shadows influence the corridors’ design (directly impacting the visually perceived
proportions of width to height, by decreasing their actual ratio). Their effect is picked up by the
photo shown in Figure B.2. The enhanced symmetry of the structure, in part the result of its
columns’ shadows, noticeably accentuates the colonnade’s perspective – the point at which all
lines (including those created by the shadows) converge.
This approximately 3pm snapshot of a colonnade oriented towards the Southeastern Winter
Solstice sunrise direction, offers an equivalent perspective at 9am for days of the year close to
the Summer Solstice. The Castle’s site view is shown in Figure B.3 from a Google Earth map. How
shadows affected the visual perception of spaces, at different times of a day, and at different
times of a year, are illustrated well by the design features of this structure.
Figure B.1. Frontal view of the Belvedere Castle on the Pfingstburg. Source: By Aaadddaaammm
- Own work, CC BY-SA 3.0,
Figure B.2. The colonnade of the Belvedere Castle on the Pfingstburg. Source: By Pine - Own
work, CC BY-SA 4.0,
Figure B.3. Belvedere Castle on the Pfingstburg, Germany. Source: Google Earth map.
Five Classical Greek Temples
Representative monuments of either the middle (6th century BC) or late (5th Century BC) Classical
Greece are the CGTs selected for analysis here. However, the features and issues associated with
these monuments, and to be elaborated next, are not confined to them. They go far beyond
these ceremony and religion related structures. Agorae, gymnasia, and other public (as well as
private) edifices and buildings also exhibit the shadows related features and visual effects
covered here.
The five chosen examples will be presented in a sequence roughly indicative of an evolution in
the sophistication and complexity on how shadows were incorporated in the site and floor plans
as well as in their superstructures’ façade and side views (their elevation plans) and cross-
sections of CGTs. Thus, a rough chronological order is followed. In selecting these five
monuments, attention was paid to their latitude of course, as well as to their elaborate and
complex structures. One of the key components of CGTs has been the various entasis (ΕΝΤΑΣΙΣ)
effects implanted onto these monuments’ crepidoma and superstructure (especially in their
peristyle and entablature). A very complex relationship is uncovered and described, regarding
the connection between shadows and the entasis effect, discussed at some length in the main
text next, and in some detail with Figure H.I.1 in the Appendix. It partly revises current views.
Temple of Hera (Temple E) at Selinunte (circa 6th millennium BC)
The earliest of the five structures to be discussed is the middle 6th century BC Temple of either
Hera or Aphrodite (in any case, a structure which has been designated as Temple E) at Selinunte
(ΣΕΛΙΝΟΥΣ) in the Southwestern coast of Sicily in present day Italy. Little is known about the exact
measures of this Temple. See Figures 1.1 and 1.2 for interior views of the Temple. Its floor plan
is shown in Figure 1.3. Of special interest here, are the two views from the interior, one in early
morning (Figure 1.1) and the other early afternoon (Figure 1.2) local time: the first shows that
the Southern colonnade’s shadows touch the base of the Temple’s cella; the second shows that
the same colonnade’s shadows touch the Northern colonnade’s base. These simple relationships
directly and firmly identify and establish beyond reasonable doubt a design connection between
shadows and the Temple’s key structural components of its superstructure.
A brief look into the rectangular dimensions of this hexastyle (meaning, with six frontal columns)
42-column peristyle Temple will be taken first. It is noted that key dimensions are as follows: at
the base of the crepidoma, this large in scale structure stretches about 67.80 meters in length,
and sports 25.30 meters in width. The Doric columns height, including the capital, is about ten
meters, see reference [2.5]. These dimensions allow, under the local angles of the Sun at Vernal
and Autumnal Equinox (Figure 1.1) and at Winter Solstice (Figure 1.2) to reach the conditions just
mentioned at around noon local time in the first case, and around 9am in the second case.
At this point certain ratios for the Temple will be computed. These ratios will work as the
benchmarks to compare the five Temples, with first and foremost being the Temple’s derived
modulus. This author computes the modulus of this Temple to have been about five meters. This
is the approximate distance between the centers of two adjoining columns’ base, and double the
total columns’ height. At their base, the columns diameter is about 1.70 meters, although this is
a very rough estimate which can’t be fully utilized in the analysis. The cella wall’s exterior is thus
about 6.50 meters inside the outer edge of the stylobate (top step of the crepidoma).
Seven key ratios for the Selinunte Temple E floor plan need be computed, and they are the
following (all seven given at a level of approximation containing three significant digits): first, the
column ratio, clr = 2.5, i.e., the number of side columns (16) over the number of frontal columns
(6), counting the four corner columns twice. Second, the ratio of the Temple’s length to width,
i.e., lwr = 2.68, a ratio quite close to 1 plus the Golden Ratio (where = 1.618….) or quite close
to the base of the natural logarithms e (where e = 2.718….) Third, the ratio of the Temple’s total
length to the lengthwise distance from the end of the pro-naos (a part of the cella) to the
stylobate, lpsr = 7/1 = 7. Fourth, the ratio of the Temple’s width to the widthwise distance from
the end of the calla to the stylobate, i.e., the ratio wpsr = 4.07. Fifth, the ratio of the Temple’s
width to the cella’s width, i.e., twcwr = 1.89. Sixth, the ratio of the Temple’s length to the cella’s
length, i.e., tlclr = 1.37. Finally, and seventh, the ratio of the total area of the Temple over the
area taken up by the Temple’s cella (counting in the cella its walls), i.e., TAcar = 2.6. It is noted
that, of course, this ratio is simply the product of the two ratios twcwr and tlclr.
Analyzing the intercolumnium - the (unequal) distances between any two columns - on either the
Eastern/Western sides, y, or the Northern/Southern sides, y’, one need solve a system of two
equations on three unknowns, where x is the Temple columns’ diameter. The system is: 6x + 5y
= 25.30, and 15x + 14y’ = 67.80. Eliminating x from the system (the 1.70m being too gross), the
following relationship is obtained: y’ = .29 + .89y, a condition resulting in the obvious result that
the frontal/back intercolumnium is greater than the side distance albeit by a very small amount.
If and only if the two lengths are approximately equal, then their measure is almost 2.64 meters,
and the Temple’s column diameter at the base is about two meters. More on this issue, and the
important ratios y/x and y’/x, will be offered in the section on comparative analysis.
We now turn to the basic Astronomy based facts of the Temple. The angle of the right triangle
that faces a side of ten meters (the Temple’s height) while the other side is 6.50 meters (the
distance of the Temple’s Southern cella wall from the edge of the stylobate), is about 57,
approximately the estimated angle of the Sun above the horizon at local 1pm time (from Figure
1.1). Here’s the computation: at Equinox, the angle of the Sun above the horizon is simply the
difference between 90 minus the location’s latitude (in this case 3734’39”N), or about
5815’21”. Since about an hour after noontime the Sun is at 57 one must conclude that the
design specifications (regarding the Temple’s three-dimensional configuration) took under
account this angle. And there’s further evidence that it did from what one observes in Figure 1.2.
At Winter Solstice, the angle of the Sun above the horizon at noon local time is simply the
difference between 5815’21” and the Earth’s tilt, 2326’13” (see the author’s computations of
the equivalent angles for Stonehenge in [1.6]). This difference is about 3449’08”. The Temple’s
dimensions imply that the distance of the Northern colonnade from the Southern side of the
Temple’s stylobate is about 23.60 meters. The angle that this length forms in reference to the
Temple’s columns’ height produces an angle of about 23. This is the approximately the angle
the Sun reaches above the horizon at about 9am local time at Winter Solstice.
Figure 1.1. Selinunte, Temple of Hera or Aphrodite (Temple E) middle 6th century BC. Interior
view, close to or early afternoon local time, towards the West. Public domain photo.
Figure 1.2. Selinunte, Temple E and the shadows of its Southern colonnade upon the Northern
colonnade’s base. Public domain photo.
Figure 1.3. Selinunte, Temple E, floor plan. North is up, with the Temple in a due East-West axis.
See text for dimensions. Public domain photo.
All CGTs incorporated features in their structure, including their columns, base and entablature
so that they accounted for visual corrections to accommodate perspective from the ground.
These corrections included columns with a tilt or tapering referred to as entasis (ΕΝΤΑΣΙΣ). This
amounted to an inward leaning of their columns, see the diagram in Figure C. Other such
corrections involved a curvature in their crepidoma and the entire entablature. In addition,
differentials in the columns’ diameter at their base, including a bulge at some level above ground
(with a maximum at around a quarter of their height from their base), and a smaller column
diameter at their capitals. All these features aimed at providing visual corrections for overall
perspective. But in addition to these structural adjustments, shadows played a key role in this
entasis characteristic. To fully appreciate that role, some additional analysis is required of entasis.
Any ground based photographic image of a Temple, taken at the level of the observer’s eye,
would show that the visual perspective is such that the columns seem to converge to a point
high above the ground, even if the columns are vertically positioned in reference to a perfectly
horizontal ground level. Inward leaning of the columns, is a form of entasis that almost all CGTs
exhibit. It was added simply to accentuate this visual perspective. In addition, given that the
perspective of observers could come from levels well below the Temples’ ground level, as is the
case of the Parthenon, situated on top of the Athens Acropolis, and the Temple of Epicurius
Apollo at Bassae, built on a local mound and at about 1130 meters on Kotylion Mountain in the
Peloponnese (both of these monuments to be analyzed in subsequent sections of this Part) could
further enhance this visual perspective of a Temple majestically pointing towards the Heavens.
Figure C. Diagrammatic representation of structure incorporated corrections onto the design of
CGTs to attain specific visual objectives regarding illusions of ‘straight lines” from the ground on
the various structural components of the edifice. Source: By Napoleon Vier from nl, CC BY-SA 3.0,
To partially counter outwardly leaning cast shadows on columns from the Temple’s entablature
and the columns’ abacus, minor inward leaning of the columns was employed. Consequently,
shadows played in fact a dual role in countering these accommodative aspects of structural
design and natural visual perspective. Without negating the primal intended illusion effects from
entasis, shadows produced a second illusion by their macro-dynamics. For a host of photos where
the shadows effect can be seen as having been incorporated into CGTs’ design, see Figure D
below, from the Temple of Hera II at Paestum, and a number of Figures in the Appendix.
The tones involving light and dark segments in shade, as well as the angle of the shadows attained
by the interplay of structures in their either carry-on or cast-off shadow capacity act as potential
counter-enforcements of these illusionary, visual effect intended to create, structural
corrections (i.e., by the slight inner leaning of the columns in this entasis case). This counter effect
is abundantly clear in Figure D, where the shadows’ angle off the entablature and the square
abacus of the columns’ capital is prominent. It in effect counters the inward tapering (tilt) in the
columns’ structural design. This is a general CGT rule, independent of specific Temples. Due to
the complementarity involved, one could possibly argue that the inward leaning columns were
put in place to partially counter the shadow effect, while still maintaining its entasis effect on
enhancing the columns perspective of convergence. More on this in the Appendix, Figure H.I.1.
Figure D. The Hera II CGT at Paestum. View from the South-East. The cast-off shadows from the
temple’s capital (specifically, its square and protruding abacus, characteristic of an early Doric
order column) produce angles of shade on the columns’ shafts, running opposite the leaning
(slope or tilt) of the columns, hence countering the tapering, one form of the entasisΝΤΑΣΙΣ)
effect of the columns’ structural design inward leaning intended to enhance visual illusions from
perspective. Photo in the public domain.
Moreover, such a shadows situation has a strong geographical, or locational effect. As the effect
(hence the importance) of shadows declines beyond the Temperate zone (the goldilocks for
shadows in design, was discussed earlier and in [1.3]), so does the ability to counter the effect of
tapering, and thus the need to invoke such means to correct for optical illusions beyond that
zone. On the other hand, it also imposes restrictions as to the optimal length of viewing a Temple
in daytime, as the counter-effect is mitigated by the shadows’ angles off noontime.
Another example concerns the thickness of the templar columns, largely dictated by a CGT’s
structural static forces. Specific thickness was needed to accommodate the vertical and lateral
forces acting on peristyle columns and in need to effectively carry the resulting loads, alleviated
by the illusion of thinner columns as a result of the vertical flutes in their column’s shaft. The
number of flutes in the Temple E’s columns shafts is twenty, as is the case in all Doric style
peristyle related columns, with one notable exception: the Hera II at Paestum, a Temple to be
viewed next; it has 24 flutes. More analysis of the complex entasis effect in the presence of
shadows is presented, when other Temples’ architectural elements are reviewed in sections next.
The two Temples of Hera at Paestum (circa middle 6th and 5th centuries BC)
At Paestum, in what is presently the Province of Salerno in the Region of Campania, Italy, on the
coast of the Tyrrhenian Sea, once comes across among other monuments the best preserved
Greek Temple of the 5th century BC. In Figure 2.1 the two Temples to be analyzed here are shown,
with the best-preserved CGT in the background. This so-called “second Temple of Hera” (or “Hera
II” built about a century after Hera I) still carries almost intact its entire entablature, which
includes in their entirety the architrave, frieze – with its triglyphs and metopes – and its two East
and West pediments, with their tympanum and sema (ΣΗΜΑ), see reference [2.6]. All columns in
both Temples’ peristyle are still standing almost intact, although their cella walls and columns
are to a large extent missing.
Both Temples are thought at present to have been dedicated to Hera, although in the past (during
the 18th century), the younger (circa 470 BC) hexastyle (ΕΞΑΣΤΥΛΟΝ) 36-culumn in peristyle
(ΠΕΡΙΣΤΥΛΙΟΝ) Temple was thought to have been dedicated to Poseidon. Both are of almost
identical in width, with the older (circa 550 BC) 9-style in front with 50 columns in the peristyle
(9x18 under double counting the four corner columns) Temple, see [2.7], being a bit longer, with
taller columns. Both have a due East-West orientation.
The two Temples’ dimensions are as follows: Hera I is about 24.50x53.50, see floor plan in Figure
2.2. Hera II has floor dimensions approximately 25x60, see floor plan in Figure 8.3. Although the
Hera I Temple has the usual Doric column shaft, each with 20 flutes, Hera II has 24 flutes in its
columns. It is apparent that the entablature and roof structure weighed far more in Hera II than
in Hera I, thus the columns having to carry far more weight, being less in number and hence with
greater distances between them, had to be quite thicker with a greater diameter in cross-section.
Figure 2.1. The two Temples of Hera at Paestum. The Temple at the foreground is the older (circa
550 BC) and the one in the background is the younger one (circa 470 BC), once thought to have
been dedicated to Poseidon. Source of photo: By V alfano - Own work, CC BY-SA 3.0,
Figure 2.2. Hera I at Paestum floor plan; North is up. Source [2.7].
Dating of the older Temple (Hera I) was essentially based on the convexity of its echinus (the
convex penultimate top column component located in the Doric order capital, supporting the
square abacus, which in turn touches the entablature’s architrave). A characteristic of the earliest
Doric Temples, the so-called “archaic” Doric order had the abacus protruding well beyond the
entablature’s surface. This is observed in both Hera I and II Temples at Paestum, and this fact has
also contributed to dating Hera I as a middle 6th century BC structure. It is noted, that as is the
case in all CGTs, the flutes of the Doric order columns’ shafts have edges so that one always faces
due East (consequently, there will be one facing due West, one facing due North, and one facing
due South.) These flutes’ orientation play directly into the hands of the architect who wanted to
exploit the carry-on shadows effects in the Temples’ design.
Figure 2.3. Hera II at Paestum; North is up. Source [2.6].
We now turn to the discussion regarding the key seven ratios of the two CGTs at Paestum and
their modulus. The Hera I Temple has the following ratios (as in the case of the CGT at Selimunte’s
Temple E, approximations contain three significant digits, and the same caveats apply in terms
of Temples’ width and length on the basis of which the ratios are computed): clr = 2; lwr = 2.18;
lpsr = 8; wpsr = 4.38; twcwr = 1.5; tlclr = 1.31; TAcar = 1.97.
Designating by x the diameter of the Doric columns at their base, and by y the distance between
two columns (intercolumnium) at Eastern front (and Western back) of the Temple Hera I, and by
y’ the corresponding distance at the (Northern and Southern) sides, one has the following system
of two equations on three unknowns: 9x + 8y = 24.50, 18x +17y’ = 53.3. Solving for y and y’ (hence
eliminating x) one obtains: y’ = 1.44 + .98y, implying the obvious result that the Northern and
Southern sides’ distance between two columns is greater than the frontal (Eastern and Western)
sides’ distance (in contrast to the result from the Selinunte Temple E, examined earlier).
As it was the case in the previous Temple, the approximations from the floor plans available are
too rough to derive conclusive results on all three variables (x, y, and y’). However, their
relationships are pretty sharp, as already demonstrated. Lack of data on the exact height of the
Paestum Temples Hera I and II, prevent an estimation of the 3-d modulus of the Temples. It is
however apparent that although with some confidence it was asserted that the 3-d modulus in
Selinunte Temple E was close to five meters, no such assertion can be made for the Temple Hera
I. The author estimates the total column height at Hera I to be close to 7.10 meters (about well
less than one meter of Hera II, estimated at around 8.30 meters). Furthermore, it can’t be
asserted that the 2-d surface modulus length and width are equal. It seems likely that the
lengthwise measure was greater than the widthwise one, since: y’ > y.
Regarding the equivalent seven ratios for Hera II at Paestum, one obtains the following results:
clr = 2.33; lwr = 2.4; lpsr = 8.15; wpsr = 4.5; twcwr = 1.8; tlclr = 1.29; TAcar = 2.32. Going through
the same calculus for the intercolumnium at the four sides of the Temple, and the estimation of
the exact diameter of the columns at the base of the stylobate, one has the following system of
two equations on three unknowns: 6x + 5y = 25; and 14x +13y’ = 60. This system offers the
following relationship between y’ and y (by eliminating the variable x, the diameter of the
Temple’s columns at their base): y’ = .13 + .393y. It clearly shows that the distance between two
columns at the long sides is greater than the intercolumnium at the short sides of the Temple.
Again, more on the ratios y/x and y’/x in the section on comparative analysis.
Attention now switches to the effect of shadows on these two Temples, Hera I and II at Paestum.
An observer, by just looking at the site plan of the monumental complex which contains the two
Temples at Paestum (along with other Temples and monuments) would immediately ask the
question: why were these two Temples positioned at the exact distance between them? The
answer becomes also immediately obvious were one to look at their aggregate (whole edifice)
cast-off shadows at critical days of a year and hours of those days.
Figure 2.4. Hera I (right) and Hera II (left) at Paestum. Aerial view from the West at local time
close to sunset. Notice that the angle of the cast-off shadow from the Northwestern corner
column of Hera I moves to the East of the Southeastern corner column of Hera II. Public domain
At Summer Solstice sunrise, the Southeastern corner column of Hera II’s long shadows are cast
so that it takes an angle such that it does not touch the Northern side of Hera I, as the shadow
falls to its West (see Figure 2.4) of the Northwestern corner column of Hera I. At Summer Solstice
sunset, the Southwestern corner column of Hera II Temple’s long shadow is cast so that it falls to
the East of the Northeastern corner column of Hera I so that it doesn’t touch the Northern side
of Hera I also. Similarly, at Winter Solstice sunrise, the Northeastern corner column of Hera I
Temple’s long shadow does not touch the Southern side of Hera II; and neither does the long
shadow from the Northwestern corner column of Hera I at Winter Solstice sunset touch the
Southern side of Hera II. In effect, the two Temples, Hera I and II, have their own unperturbed
and vital space, each shadow free from the other Temple’s structure.
Figure 2.5. Paestum, Hera I (foreground) and Hera II (background) Temples. Aerial view from
the Southeast close to sunset local time. Public domain photo.
Collectively, Figures 2.4 - 2.7 demonstrate that an effective shadow-free “vital space” surrounds
the two Temples. This vital space was drawn undoubtedly by design, dictating the optimum
spacing of the two monumental structures. One may wish to speculate as to the reasons behind
such “shadow free” space and hence the factors behind this “optimal distance” between the two
Temples. Since archeological work has pegged them to have been constructed a century apart,
one might wish to ask why in such relatively small spatial and temporal proximity two Temples
were constructed dedicated to the same goddess, Hera, as well. These are interesting
archeological and historical research quarries, but falling outside the scope proper of this paper.
Figure 2.6. Aerial view of Hera II (right) and Hera I (left) at Paestum from the Northeast. The photo
was taken at pre- (but close to) noon local time. Notice the almost straight (vertical) line linking
the Northwestern corner column of Hera I to the Southeastern corner column of Hera II. The
straight line is roughly aligned to the local Summer Solstice sunrise. Public domain photo.
Figure 2.7. Aerial View from the Southeast of Hera I (foreground) and Hera II (background) at
Paestum. The Sun is at the Southeast close to 9:30am local time. Public domain photo.
A feature hinting at this optimum spacing for shadow free spatio-temporal distancing is that
sandstone blocks and elements (now missing) of Hera I were not apparently re-used in the
construction of Hera II. Thus, reverence must have been a factor in play here, no matter the
causes which might have led to the abandonment of Hera I and the use of Hera II. Their utilization
could not have been contemporaneous. Whether natural causes, human destruction, or both,
were the forces behind the abandonment of Hera I and the construction of Hera II, almost a
century later, is not known. What can be asserted though is the conclusion that an effective
shadow free space was planned to physically separate the two Temples. In the Appendix, more
photos are supplied, pinpointing cast off shadow effects by both of these monuments, each
viewed separately (Figures H.I.1-4, and H.II.1-4) and in combination (Figures HI+HII.1-3).
In Figure 2.8 another photo of the Eastern (frontal) side pf Hera I is provided. From it, a good
estimate of the temple’s column height can be obtained. Also, the angle of the Sun’s rays can be
estimated for a late morning snapshot.
Figure 2.8. Temple of Hera I at Paestum, Eastern frontal view. The shadows cast off the Temple’s
Southern side, falling onto the interior pro-naos (part of the Temple’s cella), are shown at a pre-
noon local time. The Sun, at this moment, is at approximately a 60 angle from the horizon. From
this photograph, a good preliminary estimate for the height of the Hera I columns can be
obtained: about 6.80 meters to the columns’ abacus. It is mainly from this photo, and in
combination with other photo’s measurements that the author estimated the total height of the
Hera I columns to be about 7.10 meters. Photo in the public domain.
Figure 2.9. Close-up of a column from Hera I. Although this is an interior column, and hence no
sun (or moon) light was intended to fall on it, it demonstrates the flutes’ differential shades (in
both depth and width) creating an illusion of rotation, as the Sun traces its apparent motion from
East to West. Public domain photo.
Next, more focus is on the carry-on shadows, especially those associated with the Temples’
columns. In Figure 2.9 a column (from Hera I) is shown in a close-up. Although the column is an
interior one, thus no sunlight was intended to fall on it, it makes a general point about carry-on
shadows associated with columns that sport flutes on their shaft: as the Sun traces its apparent
Celestial motion from East to West successive flutes of the columns’ shaft obtain different
shadow depths and widths. In the case of the usual Doric 20-flute shaft columns (and given a
maximum depth of each flute within the column’s shaft) the sunlight’s motion penetrates this
depth at differing levels. This gradual depth penetration demonstrates the visual illusion of a
“rotation”, no matter the position of the observer, or the daytime. Thus, the assumed “immobile”
columns acquire a dynamic into them, allowing one to strip their static nature and presume a
“rotating periodic motion” by them. It is an ingenious way to add a sense of dynamics in an
otherwise static, immobile and inanimate object – a column.
This dynamic becomes more evident in the case of reliefs found in the friezes’ metopes, and in
pediments of CGTs. This subject will be further elaborated in the next section of this Part. Now
some more focus is directed onto the latter (circa 460 BC) Temple of Hera II. In Figure 2.10 a
longitudinal cross-section of the temple is offered; its latitudinal cross-section is found in the
Appendix (Figure H.II.1). It allows for a good estimate of the monument columns’ height – 8.30
meters to their echinus, making the Temple quite a bit taller than the about century earlier (circa
middle 6th century BC) Hera I structure. It is also notable that the top of the temple’s pediment
stands at a height above the stylobate about twice as the height of the columns’ proper. This is
shown in Figure 2.11.
Figure 2.10. A longitudinal (albeit without scale) cross-section of Hera II at Paestum. The interior
two-tier columns are shown, along the three levels of the Temple’s base. Based on the diagram,
a good estimate of the exterior colonnade (peristyle) columns’ height can be obtained: 8.30
meters to the columns’ echinus. Source: [2.10].
Figure 2.11. Hera II at Paestum. Southeastern ground view close to noon local time. The shadow
effect of the protruding pediment’s sema (ΣΗΜΑ) is noted: It offers an optical illusion,
significantly reducing the considerable height of the entablature, rendering it less “heavy”. Photo
in the public domain.
The pediment of Hera II has a triangular tympanum (this is the triangle at the top of the
entablature, which is framed by the protruding ΣΗΜΑ, and it is cupped by a cornice). That base
is projected over the rest of the entablature to such a degree that its shadow casts off onto the
entablature’s frieze and offers the optical illusion of reducing the entablature’s height and visual
sense of weight.
Moreover, as made clear from the photo in Figure 2.11, the abacus and echinus of the Temple’s
Doric columns project off the column enough so that their shadows cast off onto the column
reduces their height and at the same time clearly delineates the upper part of the Temple’s
superstructure from the weight bearing section (specifically the columns) of the lower part of the
Temple’s superstructure.
In Figure 2.12 a number of shadow effects are shown. The snapshot picks up the cast-off shadows
from the frontal set of six columns onto the area before the pro-naos, inside the Temple. In
addition, the cast-off shadow from the Northeastern corner column is shown as cast onto the
ground (lower right hand side). These two sets of shadows identify a critical set of choreographic
movements in the course of a day, under sunlight of all CGTs.
Figure 2.12. Hera II at Paestum. Aerial view from the Southeast, a snapshot at mid-morning
local time. The angle of the Eastern (façade, frontal) side set of columns’ cast-off shadows is
shown in the area in front of the pro-naos. Source: [2.10].
The Parthenon
Possibly, no other Temple (and not only among the CGTs but quite likely among all Temples in
the World) has received a larger share of modern literature (at least since the Renaissance,
possibly since Vitruvius and his De architectura” and for sure since the middle of the 19th
century) than the Parthenon. Archeologists, Historians, Architects, Engineers, Artists and Art
critics (among many other professions) have devoted an enormous effort scrutinizing every detail
possible of this indeed extraordinary structure. Many claims have been made about this
monument, some of them farfetched and poorly substantiated and documents. Yet, precious
little has been written about its shadows, let alone their effects on its design proper.
Given the time elapsed since the Parthenon’s construction, the ground it stands has undergone
transformations due to natural causes. The edifice itself has been severely impacted, impaired
by human interventions, in their vast majority malevolent. Thus, claims made today based on a
monument which time’s wear and tear and the environment have been altering for more than
25 centuries raise questions. To what extent currently obtained measurement reveal intent by
its architects and engineers to implant in it specific ratios. As is often the case, some analysts
tend to often “see” a posteriori things not intended. Especially when, the fine details of the
Parthenon’s lines and arcs in both its crepidoma and superstructure (columns, cella and
entablature) are involved. This question necessitates that one focuses on its basic elements.
As noted in the Introduction, this isn’t the forum to either exhaustively survey or even attempt
to summarize this immense volume of work. But, one may ask two legitimate questions: is there
anything left to be addressed in discussing the Architecture of the Parthenon? Of course, there
is, but as it turns out it is a bit obscure. Surprisingly, the role of shadows has been neglected
among the thousands of authors who have written about this pivotal Temple in Humanity’s
History. A second question is then: is this issue of shadows a major one for the Parthenon? It
turns out that it is. In answering these two more or less existential questions about the Parthenon
and its shadows, only subjects not addressed (to the author’s knowledge) by prior authors or
found in the existing vast literature will be explored. The analysis, as it also turns out, offers a
novel perspective regarding the so called “Parthenon Marbles” currently housed in the British
Museum and the manner they are exhibited.
Firstly, the Parthenon’s site plan will be reviewed, as the Temple sits on top of the Athens
Acropolis. The location is of course linked by History of the site to the prior Mycenaean Bronze
Age and later Iron Age temples which pre-existed (the “ΟΛΥΜΠΕΙΟΝ” and the “ΕΚΑΤΟΜΠΕΔΟΝ”)
and were supplanted by the Parthenon. However, this History still doesn’t answer in full the
question why this specific location was chosen at the Athens Acropolis site by ΚΑΛΛΙΚΡΑΤΗΣ and
ΙΚΤΙΝΟΣ, the Parthenon architects. The Temple’s construction lasted about fifteen years (447
432 BC). In a series of Facebook research posts, found in [1.7] – [1.11], the author discussed the
morphology of the Acropolis’ bedrock shaped by the Mycenaean walls, and some of the
monuments there where the subject of shadows was first discussed in reference to both the
Parthenon and the Acropolis at large. What is presented here, is a continuation of that discussion.
Figure 3.1. An axonometric rendition of the Athens Acropolis, as of the end of the 5th Century
BC. View from the Southwest. Source: [2.11].
Figure 3.2. The Acropolis site plan. Source: [2.12].
In Figure 3.1 an axonometric rendition of the site plan of the Athens Acropolis is shown, as it most
likely was looking by the end of the 5th century BC. In Figure 3.2 the actual site plan is provided,
where the Acropolis’ edifices in the course of about half of a millennium (from the 5th century BC
to the 2nd century AD – when the Odeon of Herodes Atticus was built) are depicted. From both
drawings, it is evident that the Parthenon was intended and planned to be (by far) the most
dominant element in the plan at the hilltop. No edifice was to cast a shadow at any time of the
day, at any day of the year, on the Parthenon. On the contrary, the Parthenon was constructed
at such a grand scale and location as to cast a shadow not only throughout the Acropolis during
the course of any day of the year; but in fact, cast a shadow throughout a good part of the Athens
area, North and South, East and West, close to sunrise and sunset throughout the year.
It is usually mentioned that the Parthenon has an East-West orientation. Even accounting for the
slight (a few degrees at most) change in orientation due to the change in the declination of the
ecliptic, the Parthenon was never intended to have a due East-West (that is on the Equinox East-
West axis) orientation. The reason is that the architects of the Parthenon intended to have all
sides of the monument directly hit by sunrays, from sunrise to sunset throughout the year
from the sunrise at Summer Solstice (the lowest azimuth sunrise), to the sunset at Winter
Solstice, the lowest azimuth sunset in the year). Far more on the Parthenon’s shadows in a bit.
Figure 3.3. The Parthenon floor plan. North is up, slightly towards the right (precisely indicated
by the top righthand side arrow containing symbol). Drawing in the public domain.
The reason why this was the architects’ intent will be more fully discussed in a following section,
when the role of the shadows upon the Parthenon’s frieze reliefs will be discussed. Next, we
obtain the Parthenon’s vital statistics and compute its key seven ratios. For that purpose, the
floor plan of Figure 3.3 is utilized. To be consistent, as the Parthenon’s cella (which is a term
usually employed to include the space called Naos) will also include what, in Figure 3.3, is referred
to as the “Sekos” (ΣΗΚΟΣ). Note that although the entrance to the Naos is from the East (the
usual front entrance in all CGTs), the Sekos has a Western entrance as well.
Moreover, the seven ratios are computed by keeping in mind that: (a) they are estimated by
taking as reference the top of the stylobate the top step of the crepidoma, upon which the
Temple’s superstructure rests, thus the relevant dimensions here are not the 31mx69.5m
measurements listed in Figure 3.3 (with a length to width ratio including the crepidoma - of
2.24) but about 28.90 meters wide and approximately 67 meters long; (b) the Northern and
Southern cella’s walls (that is, the Northern and Southern boundaries of the enclosed space of
the Parthenon) are assumed to commence not at its step, but at the line indicating the exterior
of the walls; and (c) specifically in the cella’s Eastern and Western sides, the walls are not where
the protruding Northern and Southern walls end, but where the Eastern and Western walls begin.
In view of these qualifiers, the seven ratios are as follows: clr = 2.13; lwr = 2.32; lpsr = 6.8; wpsr
= 6.67; twcwr = 1.40; tlclr = 1.42; TAcar = 1.98.
The height of the Parthenon’s columns is about 10.40 meters; their diameter at the base is about
1.90 meters (the four corner columns’ diameters are a bit longer). Since we do have
measurements on these two variables, we can ascertain the Parthenon’s 3-d modulus. The
widthwise modulus is evident directly from the location of the cella’s Northern and Southern
walls: the exterior lines of these two walls, if extended, cut about the center of the second and
penultimate columns of the Parthenon’s Eastern and Western sides. This fact points directly to
the widthwise dimension of the modulus as being the distance between two widthwise columns’
centers. Similarly, one observes that the imaginary line joining the end of the (extended)
Northern and Southern walls of the cella cut the 3rd and 15th column (lengthwise) at their center
as well. This fact then directly implies that the lengthwise measurement of the modulus is the
lengthwise distance of two columns’ centers.
We turn now to measuring the intercolumnium length. As the lengthwise and widthwise distance
among columns isn’t the same (as it was the case in at least two of the three Temples already
reviewed), one must compute the average distance in both sides of the peristyle separately. We
then have the system of two equations with three variables, so that 8x + 7y = 28.90, 17x + 16y’ =
67, where we do know that approximately all columns are 1.90 meters thick at their base on the
stylobate. There is an exception: the four corner columns, for which we do not have exact
measurements regarding their diameters. We do know nonetheless that they are slightly larger
than the rest 42 columns. However, they differ not by much to make a difference in what is
presented and concluded here. We shall come back shortly to this issue, regarding exactness in
measurements and Metrology in CGTs.
Consequently, given the system of two equations, we obtain: y = 1.95 meters, and y’ = 2.17
meters. As it was the case in the Temples examined thus far, the average distance between two
columns at the stylobate is longer lengthwise than the intercolumnium widthwise. Thus, we
conclude (contrary to Vitruvius’ assertion) that on its Eastern and Western sides, the Parthenon
had an intercolumnium of about 1.95 meters; whereas, at its Northern and Southern side about
2.17 meters separated two columns at their base. The unweighted (by the number of columns)
average thus intercolumnium (on all four sides) is 2.06 meters; whereas the weighted (by the
number of spaces between the eight columns East and West, and the seventeen columns North
and South) is 2.10 meters, or 1.11 times the diameter at the columns’ base on the stylobate,
contradicting Vitruvius’ assertion that the minimum intercolumnium in Greek temples was 1.5
times the columns’ diameter at their base.
Hence, connecting the intercolumnium with the modulus we derive the following: the distance
between two columns at their base widthwise is: x + y = 1.90 + 1.95 = 3.85 meters, this being the
widthwise measurement of the Parthenon modulus. Similarly, lengthwise we obtain: x + y’ = 1.90
+ 2.07 = 3.97 meters, this being the lengthwise measurement of the Parthenon’ modulus.
Assume an average of 2.06 meters, and a height of 10.40 meters for each column, one has a ratio
of about 5.05. Taking the lengthwise modulus measurement (3.97) we see that the height is 2.6
times this measurement and 2.7 times the Parthenon’s widthwise modulus length. In summary,
one is rather safe to suggest that the intended basic modulus of the Parthenon was very close
to four meters, in a ratio width to length to height of 1:1:2.5. Obviously, engineering adjustments
were made to accommodate static loads, so that very likely the engineering requirements and
construction imperfections at the margin were traded off versus aesthetic and pure architectonic
design requirements.
At this point, and since these measurements might induce discomfort among certain Parthenon
purists, a general note is needed about measurements, their accuracy, precision and exactness
in the recording of human construction. The essence of this parenthesis may be considered to be
an axiomatic statement. As mentioned, the Parthenon’s peristyle contains 42 columns that in
principle are thought to be of equal diameter and height. Furthermore, four columns (the corner
ones) are mentioned in the literature as slightly larger than the 42 (but of equal height). However,
it is also reasonable to argue that, when human carving is involved in such construction scale, no
matter the tools used, effort put into, and the method employed to attain exact replication of
such structures (in this case Pentelic marble columns, consisting of many blocks), it is next to
impossible to do so. Maybe we do not have the means yet to exactly measure these columns’
attributes in minute detail, say at the level of a tenth of a millimeter. But were we capable of
achieving such measurement level of accuracy (possibly at the tenth of a millimeter scale or
below), we can rest assured that they are not identical. In Nature, no two specimens of any
species are identical, at that level of detail, and no one should expect that human production (no
matter how perfect it might be) can produce identical products at such levels of approximation.
Not even machine-based, mass produced items are identical. At some level of detail and record
keeping approximation, there will always be some difference between any two of them. They
might be close to an average, but they are never identical. This general rule must be kept in mind,
when statements are made about any measurement, by any one, in Archeology and in
Architecture (and well beyond these two disciplines), especially when artifacts and structures of
the 6th and 5th century BC are involved, measured today. Consequently, arguments of any type
(including those advanced here) should be taken under this axiomatic principle they break
down (grossly or slightly) beyond some level of approximation.
Figure 3.4. The Parthenon’s façade (front, Eastern Entrance elevation). It is noted that the slight
entasis effect on the crepidoma is not shown. Source: [2.12].
In Figure 3.4 the Parthenon’s façade is shown. From the diagram, a number of key ratios can be
obtained, related to the edifice modulus. As derived earlier, the length and width of the modulus
was about four meters, so that the height of the Parthenon’s columns stand at 2.5 times this
length (at about 10.40 meters, on top of the stylobate). The total height of the entablature is
(from the above diagram) 6.93 meters, the pediment, including the tympanum and its sema
(ΣΗΜΑ) plus the cornice, is 4.39 meters. Their ratio (6.93/4.39) is about 1.58, a ratio close by
about two percentage points to the Golden Ratio (1.618….) The ratio (10.40/6.93) is almost
exactly 1.5. It is noted that the Golden Ratio (among other irrational number type ratios) appears
at many points and spaces within the Parthenon’s overall structure. However, it is not the
purpose of this paper to identify these spots, as the analysis here focuses on the aggregate.
Figure 3.5. The remnant of the Parthenon’s Southeastern entablature corner. Cast-off shadows
from the sema framing the pediment’s tympanum upon the frieze are shown. Also, the six shown
triglyphs of the frieze and the metope five segments, as well as the tympanum’s relief carry-on
shadows compose a scene of considerable live action – as the shadows move in the course of a
day. The choreography at the pediment is accentuated by the columns’ own dynamic shadow
motion depicted by the moving carry-on shadows at the flutes and the capital’s echinus and
abacus change in shade and tone of their own carry-on shadows. Source of photo: [2.15].
The architrave is equal in height to the frieze (which includes the triglyphs and the metopes),
their combined height being about equal to the pediment’s height. The three steps of the
crepidoma have widths so that each step corresponds to the (Southern and Northern) end of the
tympanum’s sema and the cornice correspondingly. Given that the total width of the Parthenon
including the crepidoma is 31 meters (see Figure 3.3) and the total height (measured at the very
top of the cornice from Figure 3.4) is 17.87 meters from the ground level, one obtains a ratio
(31/17.87) of about 1.73 close by two percentage points to one and three quarters, meaning that
the total length of the Parthenon’s façade is one and three quarters its total height, exclusive of
the Parthenon’s acroterium, the ornament on top of the pediment’s apex. One can easily
compute the equivalent ratios for the sides (Northern and Southern), but this is left to the
interested reader.
In so far as carry-on shadows are concerned, in Figure 3.5 a detailed view of such shadows cast
by a section of the frieze at the Southern corner of the Parthenon’s East pediment are shown.
Later, on the section regarding the reliefs of CGTs, extensive commentary is supplied regarding
the intended effects of shadows on the elements of the entablature carrying such reliefs.
Moreover, in the Appendix, a number of Figures are supplied (Figures P.1 – P.4), indicative of the
shadows’ effects applicable to the specific case of the Parthenon. It must be kept in mind that
points made about the previous Temples and their shadows will not be repeated for the
Parthenon – as they hold universal validity for all CGTs.
The Temple of Epicurius Apollo at Bassae
This extraordinary Temple (built contemporaneously with the Parthenon and, generally assumed,
by one of the two Parthenon’s architects – Iktinos) is the smallest of all five. It is different than
the previous four Temples analyzed, in two basic respects. Firstly, it contains all three column
orders, its peristyle consists of 38 Doric columns, its opisthodomos and pro-naos (see Figure 4.1,
spaces #1 and #4 correspondingly) are supported by four Ionian columns; whereas the eleven
interior columns are of the Corinthian order, with the central one having the oldest Corinthian
capital known. Secondly, it has an almost (although not exact, as it currently faces slightly to the
East, see ref. [2.18]) North-South axis and orientation, with a Northern main entrance.
Moreover, this Temple is situated at the Southernmost latitude of all five cases. Hence, the angle
of the Sun from the horizon is greater than any other Temple’s at the corresponding hour and
day, for all hours of the day, at any day of the year, resulting in comparatively shorter shadow
lengths than those of the other Temples’ corresponding hour (at any day of the year). It is a
hexastyle structure, with six columns in the front and back sides, and fifteen columns at its
Eastern and Western sides. Thus, its clr = 2.5.
Apollo the Attendant’s (ΕΠΙΚΟΥΡΙΟΣ) Temple has dimensions (at the stylobate) as follows: 14.35
meters in width, and 37.65 meters in length. Inclusive of the two crepidoma steps’ width (about
.85 in toto), these dimensions become: about 16 meters in total width, and 39.40 meters in total
length, for a ratio of (39.40/16) 2.46 a ratio very close to the Silver Ratio (2.4142…) to be
compared with the Parthenon’s equivalent ratio of 2.24. However, the key ratio for our purpose
here and to be consistent, i.e., computed without the two steps included, at the stylobate, is lwr
= 2.62. The rest of the Temple’s seven vital ratios are as follows given that the cella will be
assumed to include spaces #1 - #4 (see Figure 4.1): pnslr = 7.22; pnswr = 4.71; twcwr = 1.74; tlclr
= 1.4; and TAcar = 2.44.
Next, we tackle the monument’s modulus. Notice that, again, the outer edge of the Eastern and
Western walls of the Temple’s cella, if extended, intersects the second and penultimate columns
from the Northern and Southern (narrow) sides at their very center. Further, noticeable is the
fact that the opisthodome and pro-naos supporting columns align precisely with the third column
(from both Northern and Southern sides). Thus, the modulus grid cuts right through them, and
going through the Temple columns’ very center, strengthening the author’s view on the CGTs’
modular and grid structure..
The height of the Temple’s 38 peristyle columns is 5.90 meters (inclusive of their Doric capital)
measured from the stylobate to the entablature’s architrave, and the total height of the Temple
(at the pediment’s apex) is 10.40 meters, both (column and Temple heights) computed by the
author from the cross-section diagram offered in [2.16] and shown in Figure 4.2. The Temple’s
intercolumnium at the North and South sides y, as well as the East and West in between columns
distance y’, are given from the usual system of two equations with three unknowns, where x is
the columns’ diameter at their base. The system of two equations stated in these three variables
is: 6x + 5y = 14.35, on the narrow sides, and 15x + 14y’ = 37.65 along the longer sides.
Figure 4.1. Floor Plan of the Temple of Epicurius Apollo ΠΙΚΟΥΡΙΟΣ ΑΠΟΛΛΩΝ) at Bassae
(ΒΑΣΣΑΙ). Space #1 is the opisthodomos (ΟΠΙΣΘΟΔΟΜΟΣ) or the “rear structure” with a Southern
entrance; space #2 is the adyton (ΑΔΥΤΟΝ) which has an Eastern entrance; space #3 is the main
naos (cella); and space #4 is the pro-naos. Although the diagram above shows a perfect North-
South Temple alignment, the actual orientation of the monument is slightly to the East-
Northeast, see text for reference. Source of diagram: [2.14].
From [2.16], and the diagram of Figure 4.1, the horizontal cross-section diameter of the 38
peristyle columns is found to be about one meter, measured from the columns’ center to the top
point of the flutes’ edges. Consequently, we find that the variable y is about 1.67 meters (again,
longer than the Vitruvius’ estimate of 1.5 times the column’s diameter at the base); and variable
y’ is about 1.62 meters, quite close to (but slightly less than) the narrow side’s intercolumnium.
Consequently, the modulus of the Temple widthwise is: 1+1.67=2.67 meters; and its lengthwise
measure is: 1+1.62=2.62 meters. For all practical purposes, the surface module is a square with
sides 2.65 meters. As the height of the columns is 5.90 meters, the ratio of height to the modulus
length is 2.23. The ratio of the Temple’s total height (10.40 meters) to the modulus length is 3.92.
Thus, it is relatively accurate to state that the modulus of 2.65 meters produces: 1:1:2.25 in terms
of column height; and 1:1:4 in terms of total Temple height.
Figure 4.2. Temple of Apollo at Bassae, cross-section. Contrary to the diagram’s indication, the
columns do not consist of five layers of blocks. Each column contains grey limestone blocks of
generally uneven height, as it can be discerned from Figure 4.2.a. At their base on the stylobate,
these blocks are about one meter in diameter. Columns contain entasis in the form of a bulge at
about one third of their height from the base. Source of diagram: [2.16].
We now turn to the subject of shadows, cast by the Temple and its components. As noted
already, the latitude of Bassae is 3725’47”N. On this basis, one can obtain the highest point
above the horizon, the Sun is at local noontime during the Summer Solstice day. That angle is:
ω(SS)=760’26”. At Equinox, the angle is ω(E)=5234’13”, while at Winter Solstice the angle of
the Sun above the horizon is: ω(WS)=2808’00”. It is noted, that due to the strongly irregular
topographical features of the Temple’s location, these angles are computed on a hypothetical
flat and horizontal horizon at the level of the Temple.
Figure 4.2.a. Temple of Apollo at Bassae, Northwestern corner view. It can be discerned that each
of the Temple’s columns does not contain five limestone blocks of equal height, a fact also
detected by inspection of the two Southwestern columns’ six blocks in Figure 4.4. Some columns
contain five blocks, of uneven height, and some six (also of uneven height). Photo source: [2.19].
This is all the information we need here to make the following estimates in answering the
question: how deep into the Southern side of the Temple (the opisthodomos) does the cast-off
shadow from the architrave get. We find that at Vernal and Autumnal Equinox at noontime the
sharply delineated (not fuzzy, this being a central assumption in this paper) shadow penetrates
about 4.50 meters inside the Southern space of the Temple, the location of the two inner columns
supporting the opisthodomos, and where also the Eastern and Western walls of the
opisthodomos commence (see Figure 4.2.b, line D); at Summer Solstice, local noontime, the
shadow only penetrates about 1.45 meters the Southern side of the Temple; whereas, at
noontime Winter Solstice the shadow could reach 10.90 meters inside the Temple’s Southern
side, about where the central column of the cella is located (see Figure 4.1). Obviously, since the
cella’s Southern (opisthodomos) wall blocks that penetration, the architrave’s cast-off shadow
length could reach about a two-meter high level at the cella’ Southern wall. However, it is the
behavior of the cast-off shadows at Equinox on the Temple’s Southern side that was of critical
importance, as it was the case for the previous Temples analyzed.
Thus, it is concluded that the shadows at Equinox played a vital role in the Temple’s design. It
is noted that the length of the cast-off shadows at noontime during Equinox was also a critical
component in the design of Stonehenge Phase 3 II, circa 2500 BC, see reference [1.6]. This
particular characteristic of shadows’ role in the design of monuments supplies a direct link in
tracing the evolution of the Temples’ lineage, from the Neolithic into the Classical Greek Era.
It is noted further that, although the Temple’s peristyle columns carry entasis of the bulge type,
they do not contain the inward tilt entasis characteristic that the columns of the Parthenon and
the previous four Temples analyzed in this paper exhibit. Obviously, it did not need such inward
leaning of its columns type entasis, as it was built at such an altitude, on a mountain with steep
slopes, and locally on top of a slight topographic rise or mound. The top of the mound was
flattened, to construct the Temple (see Figure V.1 in the Appendix). Hence, the very nature of
the local topography granted the Temple the effect pursued by architects at various other CGTs,
contemporary with this Temple at Bassae, but built on smoother and flatter grounds.
Of import is the Eastern cella wall at the adyton level, and the door in it. In Figure 4.2.b the floor
plan of the Temple is shown. The angle 2ω (defined by the two red lines in the diagram) confine
the directions that allow the rays of the rising Sun to enter the cella. It is shown that the door is
positioned so as to allow at all days of the year the rising Sun’s rays to penetrate the inner
sanctum of the Temple, at the adyton. The angle is about 50. The due East-West axis, as
drawn, goes through the Temple’s critical point O, positioned at a strategic Temple entry point.
We are quite confident in asserting that the rising Sun’s rays always penetrate into the Temple’s
inner cella, because of the azimuth of the rising Sun at the Solstices. This azimuth at Bassae is
close (by a few degrees) to its latitude of about 37.5. See [1.3] for more on this point. Given the
mountainous terrane of the Bassae Region, this 2ω opening to sunrays grants validity to the claim
that this is a rather good approximation to the actual occurrence.
In Figure 4.2.b, another important angle is identified: it corresponds to the ray going through the
Eastern columns, through the door and into the Temple’s adyton emanating from point C. This
point depicts a direction which corresponds to a special hour of the day (around 9am) at which
time the sunrays go through the Temple’s 4th and 5th column (on the long Eastern side, from the
Southeastern corner) at an azimuth of about 137 (the columns forming a very narrow slit), they
penetrate the Temple’s doorway and hit its omphalos, the central interior column crowned by
the oldest Corinthian capital known to date. That column is where the space of the adyton ends
at its Northern side, and the Southern limit of the naos proper is set.
The shadow and light effects (resulting from these angles) point to a significant role the inner
Southern wall of the cella’s adyton played for this Temple, as it was directly illuminated by the
door opening at the Temple’s Eastern side. The visitor, entering the Temple’s cella from the North
would had enjoyed a light display behind the central column (the Temple’s omphalos) of
extraordinary brightness.
Figure 4.2.b. The sunrise rays at the Temple of Epicurus Apollo at Bassae as they penetrate the
Temple’s Adyton, as well as close to 9am from point C. The Temple’s floor plan is adopted from
reference [2.20], and its grid system is not consistent with the grid and modulus pattern
presented here. The Temple is assumed to have a due North-South orientation (which is an
approximation, as it has been discussed in the text). All results derived in the text critically depend
on the door’s exact location and width. Source of the final diagram is the author.
In carrying out a comprehensive review of the impact shadows had on the Temple’s design,
detailed examination of all shadows emanating from all sources is needed. This ought to include
impacts by all peristyle columns on the Temple’s superstructure elements. This enumeration
ought to include the following interplay during the day and in the course of a year: column-to-
column, column-to-cella’s walls interactions, as well as those shadow-related architrave’s
connections to the columns and the cella.
To accomplish this complex and involved task, a computer based algorithmic process is needed.
The requirements of such a comprehensive approach to the role shadows play in monuments
was outlined initially in reference [1.1] when the Mathematics of monoliths’ shadows were
presented, and in more detail in reference [1.6], for the case of Stonehenge. Selective impacts
along these lines are shown in Figures 4.3 and 4.4, as well as in Figure V.2 in the Appendix, in so
far as the Temple of Apollo at Bassae is concerned.
Figure 4.3. Temple of Epicurius Apollo at Bassae, snapshot from the Northwest. The entablature’s
shadow cast onto the cella’s Western wall is shown, at some early afternoon local time. Photo in
the public domain.
For this Temple, we shall not repeat the points made regarding shadows (either of the cast-off or
carry-on variety) already presented in the case of the previous four CGTs, with one key exception,
due to its North-South orientation. In Figure 4.3, the entablature cast off shadow upon the
Temples’ Western side is shown. Since the Temple’s long side is exposed to the West, the shadow
effects associated with Western exposure are enhanced vis a vis those with a narrow side
Western exposure. The opposite of course holds for the Southern (narrow) side exposure, in the
case of this Temple, where the optical effects are condensed. This relative emphasis could have
been reflected in the reliefs of both the friezes and the pediments of the Temple. Since few
sections remain of the Temple’s entablature, little can be inferred from (or added to) the carry-
on shadows’ impacts already discussed (and further to be added in the last section of the paper).
In Figure 4.4 the Temple’s Southwestern corner is shown, with the sixth Southern column (the
Southeastern corner column) missing. The cast-off shadows onto the fifteen Western columns
from the Western architrave are shown, to an extent countering the columns’ inward leaning
visual illusion, as expected and as extensively discussed already.
This completes the analysis of the Temple of Apollo at Bassae, which has received considerable
attention (of course nowhere near as much as the Parthenon) in the literature of CGTs. Some of
that literature is, unfortunately, of the pseudoscientific variety, as it suggests that this is a
“rotating” temple (!)
We now turn to a Comparative Analysis of these five Temples.
Figure 4.4. Temple of Apollo, SW view. Uneven in height blocks detected. Pinterest photo.
Comparative statistical analysis
Data on vital statistics and key ratios of five Classical Greek Temples
At the outset, it is noted that this section doesn’t intend to be a comprehensive comparative
analysis of CGTs, since this task is far removed from the main objectives of this limited research
effort. This section’s work is intended to indicate what such a comparative analysis could entail.
In this section, we combine all the vital statistics, which are then used to derive seven key ratios,
and derive a comparative analysis of the CGTs examined. First, the vital statistics of the five
Temples are presented in Table 1. Then, in Table 2, the derived seven ratios are shown for each
Temple. The following abbreviations will be used: Temple of Hera (or Aphrodite) at Selinunte –
SE; Temple of Hera I at Paestum - H1; Temple of Hera II at Paestum – H2; The Parthenon – P; and
Temple of Epicurius Apollo at Bassae – A.
Moreover, H will designate height of column; L will designate Temple length; W will designate
width of Temple (where H, L, and W representing counts as measured from the stylobate); M will
designate modulus; x will define the Temple’s column diameter at its base on the stylobate; y will
stand for the intercolumnium at the Temple’s narrow side; y’ will represent the Temple’s
intercolumnium at its long side. When x isn’t available or poorly estimated (and thus, y and y’ are
not available or poorly estimated also) the derived relationship between y and y’ will be stated.
For the definition of the ratios, the reader is directed to their discussion in the text (especially
the presentation of the first Temple – SE).
Table 1. Comparative vital statistics of the five Classical Greek Temples.
Temple H L W M x y y’
SE 10 67.8 25.3 5 y’=.29+.89y, y’ y
H1 7.1 53.5 24.5 ? y’=.13+.39y, y’ ? y
H2 8.3 60 25 ? y’=.14+.98y, y’ > y
P 10.4 67 28.9 4 1.9 1.95 2.17
A 5.9 37.65 14.35 2.65 1.0 1.67 1.62
From the above Table 1, one obtains the following averages: on H, the average height is H*=8.34
meters; on L, the average length is L*=57.2 meters; on W, the average width is W*=23.6 meters;
the average modulus is 3.9 meters (in all three dimensions); on the other three variables,
averages are not that meaningful, since the number of cases where the y and y’ are known (2)
are less than the number of cases where they are unknown (3).
One can of course derive more elaborate statistics, such as median, standard deviation, variance,
etc. But since this is not a random sample, and there are only five cases involved with much
variation in these vital statistics, such vital statistics’ averages would be of limited value.
However, averages become slightly more meaningful on ratios.
A note on the Temple E at Selinunte is needed: if one accepts the columns’ diameter at their base
as being close to 1.70 meters, then one obtains: y=y’=3 meters. However, this result critically
hinges on the column’s thickness approximation. Moreover, it must be noted that in the cases
where a Temple’s total length and width at the crepidoma level was used for the estimation of y
and y’, the resulting counts are not as much affected as they are by the column’s diameter
approximation. This is because in the system of two equations on three variables the Temple’s
relative magnitude of width and length is of import, not their absolute count, as the absolute
counts’ effect is mitigated in the computing.
Next, the comparative analysis turns to the seven computed ratios for the five selected Temples.
Table 2. Comparative ratios from the five Classical Greek Temples.
Temple clr lwr lpsr wpsr twcwr tlclr TAcar
SE 2.5 2.68 7 4.07 1.89 1.37 2.6
H1 2 2.18 8 4.38 1.5 1.31 1.97
H2 2.33 2.4 8.15 4.5 1.8 1.29 2.32
P 2.13 2.32 6.8 6.67 1.4 1.42 1.98
A 2.5 2.62 7.22 4.71 1.74 1.40 2.44
Averages clr* lwr* lpsr* wpsr* twcw* tlclr* TAcar*
5 cases 2.3 2.44 7.43 4.87 1.67 1.36 2.26
Initial and preliminary findings
Each CGT had its own fingerprint, no two CGTs are alike, let alone being identical. However,
computing averages and deviations from averages are important and meaningful indices to
classify CGTs and derive evolutionary trends in their design specifications. By computing the
individual Temple’s average deviation (in absolute value) from the five Temples’ group average,
one realizes that the Temple of Apollo at Bassae is the closest to an average than any other of
the Temples included in this analysis’ limited sample. Whereas, on the other end, one finds that
the Parthenon is the furthest away from the average of all five Temples analyzed.
Noted is the fact that, due to the connection between the three ratios twcwr, tlclr and TAcar,
the role of the first two of these ratios is enhanced in the computing of the averages (thus, by
extension in the overall results the influence of these two ratios is positively weighed).
In computing the individual Temple deviation from the group average by attribute, one has: for
SE, the absolute value of deviation for clr** is .2; lwr**(.24); lpsr**(.43); wpsr**(.8);
twcwr**(.01); and TAcar**(.06). The sum of these deviations is: SE**(1.74) with an average over
the seven attributes (ratios) of SE*=.249.
For H1, the corresponding deviations are: clr**(.3); lwr**(.26); lpsr**(.43); wpsr**(.8);
twcwr**(.22); tlclr**(.01); and TAcar**(.006). Their sum is: H1**(2.026), and H1*=.289.
Equivalently, for H2 one obtains: clr**(.03); lwr**(.04): lpsr**(.72); wpsr**(.37); twcwr**(.13);
tlclr**(.07); TAcar**(.05). Their sum is: H2**(1.41) and H2*=.2
For the Parthenon one has: clr**(.17); lwr**(.12); lpsr**(.63); wpsr**(1.8); twcwr**(.27);
tlclr**(.06); TAcar**(.28). Their sum in this case is: P**(3.33), and the average P*=.476.
Finally, for the Temple of Apollo at Bassae one has: clr**(.2); lwr**(.18); lpsr**(.21); wpsr**(.16);
twcwr**(.07); tlclr**(.04); TAcar**(.18). Their sum is: A**(1.04) and A*=.149.
Of special interest is the ratio lwr*. It is quite close to the Silver Ratio (2.4141…) Similarly, it is
noted that the ratio twcwr is close to the Golden Ratio (1.6180…)
It is obvious that a more complete sample is needed to derive more informative and valid results.
This ought to be a random sample derived from the Universe of CGTs. This is left to future
research. Furthermore, in acquiring a larger sample, cluster analysis can be carried out, so that
one could potentially classify CGTs by a host of attributes. All this is left to future research.
The reliefs of Classical Greek Temples and the Parthenon Marbles
General observations
Much has already been exposed about the various carry-on shadows in reference to the five CGTs
presented. Here and now, sharper focus will be drawn on the reliefs found on the friezes’
metopes and at the pediments, specifically at the tympanum part of the pediment, in CGTs.
Let us go back and review again what “carry-on” shadows are, as defined in reference [1.1]. In
the General Dynamical Theory of Shadows, stated by the author in a broad set of guidelines and
classifications adopted in the initial work on shadows, a key distinction was drawn between two
types of shadows. This classification distinguished between those shadows which are cast by an
object, be that an edifice, i.e., an aggregation of components with each component being able to
cast shadows on another component of the edifice or the ground; or be that an individual
component (such as, a monolith, menhir, orthostat, pillar, on a stand-alone column) that can cast
a shadow on some other stand-alone component, a wall, or the ground.
These cases’ shadows were classified as “cast-off” shadows. In [1.2] further analysis showed that
such “cast-off” shadows demonstrate fuzziness. The Mathematics and Physics involved in the
fuzzy nature of shadows were also stated in [1.2]. Since fuzziness will not be directly a factor in
the type of shadows (the carry-on variety) we are about to delve, this property of shadows will
not preoccupy the analysis here any further.
What will be undertaken here is some discussion involving this particular class of shadows, the
“carry-on” variety, which remain short in length and width thus do not exhibit fuzziness to any
meaningful extent. These are the types of shadows that are cast by individual components of an
edifice, and remain on the surface of the element or base or surface from where they emanate.
An example of this type shadows is the shadow cast by the reliefs of a frieze or the sculpture
found at a pediment’s tympanum. This type of shadows shall be the focus of the discussion that
follows. These shadows stay on their support structure, they do not migrate far from the origin
of the shadow. As such, they produce relatively “sharply delineated” shadows – since they do not
travel far from their base, this being a necessary component to generate fuzziness in the
shadows’ trails. This relative immobility of carry-on shadows doesn’t mean that their shadows
are fuzziness-free. However, the degree of fuzziness involved in their shadows’ trail is significantly
less than that of the cast-off variety.
Before we enter the discussion proper of carry-on shadows, another attribute of shadows,
analyzed in [1.1] must be recalled: the shadows macro and micro-dynamics. Shadow macro-
dynamics occur when one records the motion in an object’s cast off shadow as it moves through
the sun-lit (or moon-lit) part of the day, or over the course of a year. Whereas, the shadows’
micro-dynamics occur when, in the course of seconds, shadows move, as one is either observing
or recording them (through a highspeed camera). This type of micro-dynamics is a factor in the
“quantum nature” of shadows, as discussed in [1.2]. However, again, this will not be an issue
addressed here in any further depth.
The reason why carry-on shadows are of interest is the same as the reason why cast-off shadows
are of interest: they demonstrate a choreography around them, an interaction with other parts
of the ensemble to which they belong (in this case, the other figures depicted on a frieze or
tympanum) and their respective carry-on shadows. In effect, these carry-on type shadows add
mobility to their base surface configurations (again, with a focus here remaining on the friezes
and the tympana of Temples’ entablatures).
Of course, another element of Classical Greek Temples where carry-on shadows play a significant
role is their columns. Columns which, on their shaft, have flutes in the form of vertical stripes.
Columns constitute prime examples, where carry-on shadows appear as the tip of their flutes’
cast-off shadows fall within their arced convex recesses. These shadows remain on the columns,
they are of the carry-on type. These specific carry-on shadows have been pointed out numerous
times in the previous sections of this paper, as well as in the Appendix, with examples taken from
almost all the Temples analyzed. Not much will be added now on this angle of the issue. Here,
again, the focus will be on the friezes and the tympana of Temples.
As a consequence of the carry-on shadows’ choreography, and the motion implanted onto the
reliefs that generate carry-on shadows, these renditions in Temples’ friezes and tympana acquire
properties of a living entity, in effect these reliefs become live organisms that move. They cease
to be immobile, and as a result they do cease to remain inanimate objects. Of course, this mobility
occurs as long as they are subjected to a moving light source, the Sun (an apparent motion due
to the Earth’s rotation about its axis) or the Moon (in a very complex combination of both the
Earth’s rotation about its axis as well as the Moon’s orbit around the Earth) when either could
shed light on monuments. Thus, it is this moving light source (in its regular but complex cyclical
motion, especially in the case of the Moonlight light in effect from the Sun reflected off the
Moon’s surface) which is behind the shadows’ motion and the visual illusion of a moving relief
representation. The importance of a moving light source for carry-on shadows will be expanded
further in the next and last section of this paper.
It must be naturally noted that the motion of shadows (of either the cast-off or carry-on variety)
are not fast motions. They are in effect quite slow movements – and no person stands still
watching shadows move, as no one watches grass grow, as the popular expression goes.
However, what is of importance here is the fact that although the mobility of shadows remains
imperceptible in the relatively short span of a few minutes, it does not do so over extended time
periods (for example, an hour’s span). This change in the position of shadows is perceptible.
Perceptible change in shadows is a major component why human spaces (both indoors and
outdoors, in day under sunlight or night under moonlight) contain a requisite variety which makes
them livable.
Shadows are means of rendering spaces pleasant and suitable for living, as much as light itself is,
the source that produces these shadows. As discussed in the General Dynamical Theory of
Shadows in [1.1] there’s a complementarity between light and shadow. Simply put, if the
shadows were to be totally eliminated, that would mean that the source of their existence – light
– would be totally eliminated. There can’t be life without shadows, as much there can’t be life
without light.
Moreover, a moving light source produces moving shadows, and this attribute of mobility renders
the objects which cast shadows or a surface that shadows are cast against even more valuable to
a living space kind of environment. In fact, without mobility in it, the source of shadow (the object
called here a relief”) is an inanimate dead object. It is precisely this attribute of shadows and
their ability to grant anime to the objects they emanate from, specifically of the carry-on variety,
which shall be discussed more extensively next with a special reference to the Parthenon
Figure 5.1. The Parthenon, Western pediment, Northern corner sculptures. Source: [2.21].
A Note on the Parthenon Marbles
The following discussion can be construed as a follow-up to the author’s Facebook research post
of February 10th, 2017, reference [1.9]. So, what is about to be discussed next, draws from both
the analysis presented above in this paper as well as from [1.9]. In addressing specifically reliefs
related shadows, an angle is taken regarding the Parthenon Marbles (currently housed in the
British Museum along with some marble friezes from the Temple of Apollo at Bassae and many
other sections from friezes and tympana of Greek temples from various locations in the Helladic
space, including other edifices from the Athens Acropolis) which has not been taken by anyone
One of the central achievements of Classical Greek Sculpture has been the addition of a sense of
dynamic movement into them. The posturing of the person(s) depicted by the sculptures and
reliefs in Classical Greece is characterized by a deliberate sense of movement depicted by the
posture of the person rendered in the artifact’s form and the person’s attire. Shadows, are
intended to further build onto this sense of reliefs or sculptures’ dynamics.
The observer of such an object is to get the distinct and vivid impression that the person is
moving, and shadows are there (implanted into the rendition’s design) to showcase and
accentuate the impression from that motion. Especially so in the case of reliefs, see the preamble
photo of this paper (depicting a section of the Parthenon’s Western frieze), the part of the marble
frieze from the Temple of Apollo at Bassae in the Figure on p. 7, and Figure 5.1, in which
sculptures from the Northern corner of the Parthenon’s Western pediment are shown. In all
cases the role of shadows is very impressive, and an integral part of the composition.
As already noted, the Parthenon’s orientation was chosen so that all sides were to receive Sun
(and Moon) light through the day (or night) for all days (or nights with moonlight) in a year. And
in the course of the day, at different times, shadows would alter their positions, form, and
locations, so that they would present different configurations of the persons, animals and objects
depicted in the friezes and pediments. It was intended by the reliefs and sculpture makers that
shadows would add the element of change in these sections of the Temples’ superstructure.
Configuring a composition in 3-d, by carving a sense of dynamics into reliefs and sculptures, was
a great achievement by and on itself in Classical Greek Art. Effectively adding onto an object the
dynamics of the shadows’ impacts was most likely the finest attainment in 3-d of still Greek Art.
This paper will not address the legality of propriety of the destructive act of brutally removing
the Parthenon Marbles (or all the other marble pieces from all other Greek Temples) from their
original and intended locations and site(s). What this analysis makes clear is that their current
place into a Museum, under an artificial static light source, subtracts from them their very sense
of intended movement. In effect, this arrangement stifles them, it renders them immobile.
Hence, it deprives them from their life-granting element, their oxygen: sunlight and moonlight
and their motion. The agency that removed them from their intended place on the Parthenon
took away the regular periodic cycles of their motions. In effect, it suffocated them. It killed them.
Friezes and sculptures were meant to exist under a moving light source, generating their
absolutely essential dynamic moving shadows. They can only live on their Temples’ entablature.
Inside museums, they become fossilized remains of once living organisms. Removing the
Parthenon (and all other) Marbles from one Museum to put them into another simply isn’t the
line of life they need to come alive again. Other, far more architectonically bold actions are
needed, none better than installing them in situ in their originally intended location and position.
Conclusions and Suggestions for further Research
A number of conclusions can and have been reached from the analysis presented, and also some
suggestions can be derived regarding possible future research on the topics covered by this
paper. In terms of conclusions, central is the realization that shadows, in their multiple
manifestations, played a key, important and quite likely major role in the very design of Classical
Greek Temples. Their effect was anticipated and accounted for by the Temples’ architects, and it
was implanted in the Temples’ morphology. Shadows played in fact a pivotal role, not only in the
broader form and function of CGTs, as it was shown to be the case regarding the built-in entasis
characteristic of their superstructure, but also in the detailed iconography of their reliefs and
sculptures. Another important finding was the link discovered to exist between the shadows cast
by the Temples’ architrave onto their Southern side, at noontime during Equinox. This linkage is
shared by Stonehenge Phase 3 II. It is a link between CGTs and Neolithic monuments, the deepest
roots of Classical Greek Architecture. The paper also uncovered the roots of the Doric order
columns traced to the tombs at Beni Hassan, Egypt. It also traced the origins of Temples with
masonry colonnade construction to the Temples at Karnak, although the form proper of CGTs
can be traced to the Uruk Eanna District monuments.
In summary, intentional use of shadows rendered a periodic choreography to the otherwise
immobile structure of the Greek Temples and its various subcomponents. The element of motion,
a key achievement of Greek Art - which advanced reliefs and sculptures morphological
composition by incorporating a sense of movement in it, was accentuated by the theatrical role
cast-off and carry-on shadows’ dynamics added onto them. Detailed measurements of central
features of Greek Temples were needed and were collected for five selected Classical Greek
temples to specifically identify the impact of cast shadows by and to their superstructure.
Preliminary and initial comparative analysis was carried out, employing the obtained data, with
regards to these Temples’ vital statistics and key ratios (proportions in their aggregate design).
Numerous are the possible avenues for extending the work presented in this paper. Further work
regarding a more comprehensive review of the Temples’ multiple shadow effects (involving both
the entire Temple’s structure, as well as the specific shadow effects of their interacting, through
shadows, subcomponents (peristyle, cella and entablature) in their superstructure, is of course
central in these extensions. In addition, by selecting a random sample from the universe of
Classical Greek Temples, and then by deriving their vital statistics and key ratios, possibly
increasing the number of ratios considered, future research could supply a more holistic view of
CGTs than the one already obtained in this paper.
Extending the work outlined here would hopefully further enhance the already rich literature on
Classical Greek temples, as well as add impetus to the study of shadows in general. As is the case
with prior papers by this author (on Architecture, Astronomy and Archeology) this paper too was
written for the general public with College level mathematical and astronomical background.
Obviously, more detailed analysis is needed by specialist in all of the aforementioned fields.
Appendix: More Photos and Analysis of the five Temples with their Shadows
Photos of Hera I at Paestum with shadows
Figure H.I.1. Temple of Hera I, Southwest view. Early morning photo with the sun in the SE. The
flutes’ carry-on shadow casting on the columns’ shafts provide the optical illusion of thinner
columns. The 20 (or 24) flutes in the Doric order have edges identically oriented in all columns,
with one always pointing due East (thus, with one pointing due West, one due North, and one
due South). The resulting different depths in the columns’ carry-on shadows, in combination with
the angle of shadows cast off from the architrave and the abacus upon the columns, counter that
particular attribute of entasis (ΕΝΤΑΣΙΣ), which calls for inward leaning columns. A characteristic
in construction and a design tool used in CGTs, sports columns in a colonnade having a minor
inward leaning. This leaning is intended by the architect to enhance a perceived optical illusion
that an observer looking at straight up columns will perceived them as collectively leaning
inwardly, due to visual perspective, their extension meeting at a point above the Temple. The
complementarity of the shadow angle argument may point the opposite direction, i.e., the intent
by this form of entasis was to counter the illusion created by the outward leaning of the shadows
on the columns. This is the now revealed double play of shadows on the entasis effect. In
addition, the sharp transition from the shadows cast off the Western side of the square abacus
of the Doric columns’ capital to the light falling on the frontal (Southern) side is contrasted by the
gradual transition shadows undergo along the columns, due to their flutes. Public domain photo.
Figure H.I.2. Temple of Hera I, view from the Eastern frontal side. Photo taken at late morning
close to noon local time. The cast-off shadows from the front section of the entablature onto the
pro-naos columns is shown. Moreover, the cast-off shadow from the Northern section of the
entablature and the columns’ square abacus onto the columns themselves is highlighted at right.
Finally, the shadow from the interior pro-naos columns onto the Northern columns is also picked
up in this Public domain photo.
Figure H.I.3. Hera I, Northeastern view, making more evident the effects of Figure P.I.2.
Figure H.I.4. Temple of Hera I, close-up view from the Northwest of the Temple’s Northern side.
Afternoon post Vernal Equinox but pre-Summer Solstice shot. The columns’ abacus shadows are
evident on the columns, breaking their length. Public domain photo.
Photos of Hera II at Paestum with shadows
Figure H.II.1. Latitudinal cross-section of the Temple of Hera II. Source [2.9].
Figure H.II.2 The frontal side (façade) – elevation - of the Temple of Hera II. Source [2.9].
Figure H.II.3. Southeastern view of Hera II Temple, afternoon local time. Photo in public
Figure H.II.4. Northwestern view (backside) of the Hera II Temple. A number of shadow effects
are present in this early afternoon local time snapshot. Starting from the top, the protruding
ΣΗΜΑ (the frame of the pediment’s tympanum, i.e., of the equilateral triangle which crowns the
entablature of the Temple) is evident by its casting shadows both onto the tympanum itself as
well as onto the entablature’s frieze (metope and triglyphs). Then, the shadows cast off the
columns’ capital onto the column’s body proper is noted. In turn, the cast-off shadows by the
columns onto the cella’s components (columns and wall) is shown. Finally, the graduating degree
of depth in shadows cast by the flutes onto the shaft are highlighted in this photo, which is in the
public domain.
Photos of both Hera I and II at Paestum with shadows
Figure H1+H2.1. The very long shadows at close to sunset of Hera I and II at Paestum – aerial view
from the Northwest. Source:
Figure H1+H2.2. A ground snapshot from the Southeast of the complex of the two Hera
Temples at Paestum. Public domain photo.
Figure H1+H2.3. Google Earth map of the two Temples of Hera (I and II). The slight East –
Southeast (off the due east-West axis), the author asserts, is to some extent due to the Earth’s
axis of rotation motion in its 26K-year cycle, the obliquity of the ecliptic.
Photos of the Parthenon with shadows
Figure P.1. The Parthenon’ Northern and Western sides, which face Mounts Aigaleo (NW) and
Parnitha (N) and the Saronic Gulf (W), from the Northwest; late afternoon local time snapshot.
The choreography of the Western side colonnade onto the ΣΗΚΟΣ is depicted. Also, counter-
entasis effect by the cast-off shadow by the abacus onto the top of the columns on the Northern
side is shown. Moreover, the cast-off shadow by the base of the ΣΗΜΑ onto the entablature’s
frieze on both the Northern and Western side are shown. In combination, these shadows produce
a movement for the entire edifice, as their motions and macro-dynamics trace a choreographic
movement on the structure. Photo in the public domain.
Figure P.2. The Parthenon’s Eastern side, which faces (the source of its marble) Mount Pentelicus
(NE) and Mount Hymettus (E). Mid-morning snapshot from the Northeast. An apotheosis of the
carry-on shadows, as all are in full display. The columns’ flutes in combination with the lighted
frontal end of their abacus, the triglyphs’ shadows, and the base of the pediment’s cast-off
shadow offer and add a dramatic choreography of movement onto the structure. That
choreography was complimented by that implanted onto the tympanum’s reliefs absent at
present. The movement on the Eastern side lasts till noon, as it picks up the baton from the early
morning choreography on the Northern side. Then the choreography continues in the afternoon
on the Southern and Western sides. Public domain photo.
Figure P.3. Parthenon, East façade. The cast-off shadows from the abacus create a set of eight
parabolas on the columns’ shaft. The elongating effect of a pointed lighted column adds to the
illusion of a slender column. Photo in the public domain.
Figure P.4. The Western side of Parthenon facing the setting sun, as the eight frontal columns
cast off their shadows onto the six smaller columns at the entry section of the ΣΗΚΟΣ. A dramatic
choreography of successive layers of dynamics in shadows adding life and motion to otherwise
immobile bodies. Source of photo: [2.13].
Photos of the Temple of Epicurius Apollo at Bassae
Figure V.1. The location of the Temple of Apollo at Bassae; the low local mound on which the
Temple is built at an altitude of about 1130 meters on Mount Kotylion in the Peloponnese. The
snapshot is towards the Southern narrow side of the (covered) Temple. Source of photo: [2.17].
Figure V.2. Norther side view of the Temple of Apollo at Bassae. Noticeable is the tone in
shadows creating the two corridors (East and West of the Temple’s cella. Public domain photo.
Author’s work
[1.1] Dimitrios S. Dendrinos, 24 January 2017, “The Mathematics of Monoliths’ Shadows”, The paper is found here:
[1.2] Dimitrios S. Dendrinos, 1 March 2017, “On the Fuzzy Nature of Shadows”,
The paper is found here:
[1.3] Dimitrios S. Dendrinos, forthcoming, “The Dynamics of Shadows at and below the Tropic
of Cancer”, The paper is found here:
[1.4] Dimitrios S. Dendrinos, 25 November 2016, Gobekli Tepe: a 6th millennium BC monument”, The paper is found here:
[1.5] Dimitrios S. Dendrinos, 15 November 2016, “In the Shadows of Carnac’s Le Menec Stones:
a Neolithic proto supercomputer”. The paper is found here:
[1.6] Dimitrios S. Dendrinos, 14 March 2017, “On Stonehenge and its Moving Shadows”, The paper is found here:
[1.7] Dimitrios S. Dendrinos,
[1.8] Dimitrios S. Dendrinos, 18 February 2017,
[1.9] Dimitrios S. Dendrinos, 10 February 2017,
[1.10] Dimitrios S. Dendrinos, 15 June 2016,
[1.11] Dimitrios S. Dendrinos, 8 June 2016,
Other sources
[2.1] David Smyth, 2017, “Taoslin: a different perspective”,
[2.2] G. Terence Meaden, 2017, “Dromberg stone circle, SW Ireland: design plan analyzed with
respect to sunrises and lithic shadow-casting for the eight traditional agricultural dates and
further validated by photography”, forthcoming in the Journal of Lithic Studies.
[2.3] The megalithic portal:
[2.4] Simon Newcomb, 1906, A Compendium of Spherical Astronomy, MacMillan, New York.
[2.5] E. Lippolis, M. Livadiotti, G. Rocco, 2007 Architettura greca: storia e monumenti del mondo
della polis dale origini al V secolo.
[2.14] By derivative work: MaEr (talk)Bassai_Temple_of_Apollo_Plan-fr.png: User:Bibi Saint-Pol,
which is based on work of fr:Utilisateur:Papier K - Bassai_Temple_of_Apollo_Plan-fr.png, CC BY
[2.19] By Olecorre - Own work, CC BY-SA 3.0,
The author wishes to acknowledge the contributions made to this paper through his interaction
with members of the Megalithic Portal website ( ). The
author wishes to thank the site manager Andy Burnham; and also, the members of the sub-group
in it “Do you look at the shadows”. Within this group, in specific, the author wishes to recognize
the contributions by David Smyth (Energyman), Neil Wiseman (Feanor), and Richard Bartosz
(Orpbit). David Smyth has been instrumental in encouraging the author to participate in that
group, and for introducing the author’s prior work to the group members. A number of others,
including those under the literary pseudonym of cerrig and drolaf, have also contributed to the
formation of the author’s views and his study of shadows.
Furthermore, the author wishes to recognize his Facebook friends and especially those who are
members of the seven groups the author has created and is administering. Their continuous
intellectual and artistic stimulation and support have been remarkable, and thus a great sense of
gratitude is extended to them as well. Special mention must be made to Professor Terence
Meaden for his contribution, and especially his work on the shadows at Drombeg and
But most important and deer to this author has been the more than 20 years of encouragement
and support he has received from his wife Catherine and their daughters Daphne-Iris and Alexia-
Artemis. Their continuing assistance and understanding for all those long hours he spent on doing
research, when he could have allotted time with them, this author will always be deeply
Legal Notice on Copyright
© The author, Dimitrios S. Dendrinos retains full legal copyrights to the contents
of this paper. Reproduction in any form of parts or the whole of this paper is
prohibited, without the explicit and written permission and consent by the author,
Dimitrios S. Dendrinos.
... The three PPTs examined were: (7,24,25), (11,60,61), and (13,84,85). They were selected because their hypotenuse is close to their long side -an attribute exhibited by the four Parthenon right triangles, but especially triangles (CAB) and (FEG). ...
Full-text available
A novel view of the Parthenon’s structure is taken in this paper. Instead of analyzing the Parthenon’s final configuration, either in its various reconstructions or in its current condition, the study draws the Temple’s 3-d skeletal structure. Based on that sketch plan, the Parthenon’s modulus and its grid pattern are derived. In closely examining this skeletal morphology, a number of findings emerge. The Parthenon was built on the basis of a critical ratio and a set of inter-connected angles, generated by following a set of instructions. Utilizing the sketch plan (the Parthenon’s skeleton), the paper provides a mathematical optimization formulation, involving an objective function and a set of constraints. On the basis of that problem, one can derive, through the associated efficiency conditions, the entire Parthenon structure. Along the way, some topics of mathematical interest are presented and partially elaborated. Suggestions for further research are also provided.
Full-text available
This short paper’s limited objective is to provide the temporal dynamics of shadows for locations on the Earth’s latitudes close to, on and below the Tropic of Cancer in the Northern Hemisphere, as well as on the Earth’s Equator. It sets the stage for presenting the dynamics of shadows’ lengths in the Earth’s Temperate zone, within the framework of which the intended role of shadows implanted on the Classical Greek Temples (discussed in the paper of reference [1.6]) is to be set. Here, subjects such a basic bifurcation, phase transitions and the overall dynamics of monoliths’ shadows within the 0  to 23  26’13”N of Earth latitudes are analyzed and the qualitative features of their lengths’ changes over the course of a day and a year are shown, for the case of Sun-induced shadows with sharply delineated borders. The paper sets the stage for highlighting the importance of the Temperate Zone’ shadow qualities in the rise of Classical Greek Temples, to the extent that shadows were incorporated into their design proper.
Full-text available
The paper analyzes the monument of Le Menec at Carnac, in Brittany, France. It advances a number of propositions, key among them being that the strings of stones at Le Menec are not linear parallel alignments but converging arcs. These stones and strings performed a variety of cultural functions. Arcs acted as a Theme Park for celestial objects and their orbits. It is suggested that Le Grand Menec, Kermario, Kerlescan, and Le Petit Menec represented the four seasons. The paper also suggests that the stones' shadows were used as part of sundials. Each stone was used as a computing device, and collectively they constituted a proto Neolithic supercomputer.
Full-text available
The paper presents both an introduction to the theory of shadows and their mathematics, with a concentration in the cast-off shadows from megalithic Neolithic monuments. It is addressing lengths of shadows' dynamics above the Tropic of Cancer at the Northern Hemisphere. A companion paper presents the length of shadows' dynamics at and below the Tropic of Cancer here:
Full-text available
The paper addresses the fuzzy nature of shadows cast by Neolithic monuments. It presents a mathematical theory of fuzzy shadows, and extends a previous paper by the author of a General Dynamical Theory of Shadows. That original paper is found at the site here: and also here at here:'_Shadows
Full-text available
The paper documents the date for the initial construction phases of Layer III of structures D (middle 6th millennium BC) and structure C (end of 6th millennium BC - beginning of 5th millennium BC) at Gobekli Tepe. It is a sequel to the author's September 19, 2016 paper "Dating Gobekli Tepe". It uses comparative Architecture and Design analysis from Catalhoyuk and Nevali Cori as well as Jerf El Ahmar for the dating process. It also employs Alexander Thom's schema of classifying stone enclosures, by appropriately expanding it and applying it to Gobekli Tepe. The paper also traces linkages between Gobekli Tepe, Carnac, Malta, Stonhenge and Menorca.
Full-text available
The paper analyzes the Stonehenge Phase 3 II Architecture, modular structure, and their connection to the sun-induced cast-off shadows from its sarsens, and the motion of the shadows over the course of a day and throughout the year. It establishes that a direct link exists between the size of certain shadows and the design of the monument. It further documents that besides the summer solstice sunrise alignment, the vernal and autumnal equinox alignment was a major one in the monument's design. Moreover, the paper demonstrates that the Trilithons sarsens ensemble's quasi-elliptical form is a type belonging to an extension of the Alexander Thom's classification of stone enclosures.
A new survey of Drombeg Stone Circle and accurate analysis of shadow effects beginning at particular sunrises of the calendar year has led to a breakthrough in the understanding of lithic symbolism and the intentions behind the construction of this and other Irish monuments including Knowth and Newgrange that also have astronomical alignments. At Drombeg specific standing stones play critical roles at sunrise for all eight of the festival dates as known traditionally and historically for agricultural communities and as now inferred for prehistoric times following the present observation-based analysis. Crucial for Drombeg in the summer half of the year is the positioning of a tall straight-sided portal stone such that its shadow at midsummer sunrise encounters an engraving on the recumbent stone diametrically opposite. During subsequent minutes the shadow moves away allowing the light of the sun to fall on the carved symbol. It is the same for sunrises at Beltane (May Day), Lughnasadh (Lammas), and the equinoxes when shadows from other perimeter stones achieve the same coupling with the same image, each time soon replaced by sunlight. For the winter half of the year which includes dates for Samhain, the winter solstice and Imbolc, the target stone for shadow reception at sunrise is a huge lozenge-shaped megalith, artificially trimmed. Moreover, for 22 March and 21 September there is notable dramatic action by shadow and light between a precisely positioned narrow pillar stone and the lozenge stone. As a result, at sunrise at Drombeg eight calendrical shadow events have been witnessed and photographed. This attests to the precision of Neolithic planning that determined the stone positions, and demonstrates the antiquity of the calendar dates for these traditional agricultural festivals. Discussion is held as to what the concept of shadow casting between shaped or engraved stones at the time of sunrise may have meant in terms of lithic symbolism for the planners and builders. This leads to a possible explanation in terms of the ancient worldview known as the hieros gamos or the Marriage of the Gods between Sky and Earth.
A new survey of Drombeg Stone Circle and accurate analysis of shadow effects beginning at particular sunrises of the calendar year has led to a breakthrough in the understanding of lithic symbolism and the intentions behind the construction of this and other Irish monuments including Knowth and Newgrange that also have astronomical alignments. At Drombeg specific standing stones play critical roles at sunrise for all eight of the festival dates as known traditionally and historically for agricultural communities and as now inferred for prehistoric times following the present observation-based analysis.Crucial for Drombeg in the summer half of the year is the positioning of a tall straight-sided portal stone such that its shadow at midsummer sunrise encounters an engraving on the recumbent stone diametrically opposite. During subsequent minutes the shadow moves away allowing the light of the sun to fall on the carved symbol. It is the same for sunrises at Beltane (May Day), Lughnasadh (Lammas), and the equinoxes when shadows from other perimeter stones achieve the same coupling with the same image, each time soon replaced by sunlight. For the winter half of the year which includes dates for Samhain, the winter solstice and Imbolc, the target stone for shadow reception at sunrise is a huge lozenge-shaped megalith, artificially trimmed. Moreover, for 22 March and 21 September there is notable dramatic action by shadow and light between a precisely positioned narrow pillar stone and the lozenge stone.As a result, at sunrise at Drombeg eight calendrical shadow events have been witnessed and photographed. This attests to the precision of Neolithic planning that determined the stone positions, and demonstrates the antiquity of the calendar dates for these traditional agricultural festivals. Discussion is held as to what the concept of shadow casting between shaped or engraved stones at the time of sunrise may have meant in terms of lithic symbolism for the planners and builders. This leads to a possible explanation in terms of the ancient worldview known as the hieros gamos or the Marriage of the Gods between Sky and Earth.
On the Fuzzy Nature of Shadows " , The paper is found here: https://www.academia
  • Dimitrios S Dendrinos
Dimitrios S. Dendrinos, 1 March 2017, " On the Fuzzy Nature of Shadows ", The paper is found here:
The Dynamics of Shadows at and below the Tropic of Cancer
  • Dimitrios S Dendrinos
Dimitrios S. Dendrinos, forthcoming, "The Dynamics of Shadows at and below the Tropic of Cancer", The paper is found here: _of_Cancer