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The Great Pyramid’s conspicuous speed of light latitude is no accident
Robin James Spivey
Earth & Sun Association, Omega Society
y.gofod@gmail.com
The Great Pyramid was built ∼4500 years ago but a neighbouring monument exhibits
considerably greater signs of ageing. Sea levels were appreciably lower at the end of the
Ice Age when Giza was situated at the intersection of the lengthiest geodesic and par-
allel over land, a record the carving of the Sphinx appears to have commemorated. The
Sphinx patiently weathered a hostile climate until the Great Pyramid was constructed,
whose latitude in degrees tallies with the speed of light, c=299,792 km·s−1, to six
significant digits. The pyramid’s geometry showcases both πand the golden ratio, φ,
with the conjunction π−φ2≈π/6≈φ2/5 not only providing a natural basis for the cu-
bit/metre ratio but also approximating the speed-of-light latitude in radians. Its scaling
reflects the size of the Earth and its rotation rate. By relating cubits to metres and days to
seconds, this mighty monument quite deliberately encodes the value of c, figuratively
permitting the conversion of energy to mass. Parallels exist with a recent analysis of
Avebury, which also demonstrates ancient knowledge of modern physics.
Introduction
It was recently pointed out that the 5,000 year old henge at
Avebury situated at latitude 2π/7 radians might have been de-
liberately constructed as a tribute to a cluster of astronomical
events closely coinciding with the 2016 summer solstice, con-
veying not only ancient knowledge of the Earth’s geography
and orbital mechanics but also precognition of modern par-
ticle physics. Highlighting the importance of investigating
facts that seemingly imply the ‘impossible’, this work now
turns to address the Great Pyramid of Giza, finding that it also
unambiguously encodes information hitherto regarded as the
exclusive preserve of recent human generations.
Phi in the sky, Pi on the ground
The construction of the Great Pyramid at Giza was an as-
tonishing achievement, possibly completed in just a single
generation during the 26th century BC. It is the oldest of
the Seven Wonders of the Ancient World, and the sole re-
maining example. At the time of its erection, primitive ir-
regular ditches were still being dug in the British Isles using
antler picks. Whereas Stonehenge may have been magneti-
cally aligned to Avebury and Glastonbury Tor, the pyramids
of Giza are aligned within 0.05◦of true north. How was this
possible? The pyramids themselves suggest an answer.
The ancient Egyptians had a fascination for the circum-
polar stars owing to their perpetual presence in the night sky,
never dipping below the horizon. On a clear night, a star
near celestial north can be visually aligned with the apex of
a pyramid. Observers can record their location on the ground
and repeat the process as the chosen star circles the skyward
projection of the Earth’s rotation axis. A line between the
mean of this distribution and the pyramid’s apex can provide
reliable alignment to true north, even if it is not understood
that the world is spherical and spinning around an axis whose
orientation changes little during a human lifespan. The star
Thuban was closely aligned with celestial north around the
time the Giza pyramids were constructed but this method of
determining north could also have been used with brighter
circumpolar stars too such as Kochab or Mizar. The main
caveat is that the gradient of the pyramid should exceed its
geographical latitude. For the Great Pyramid, an observer on
the ground would be standing almost 250 m from its apex and
an inaccuracy of 0.05◦would equate to a transverse offset of
200 mm, exceeding the interpupillary distance in humans.
The circumference of a circle divided by its diameter is
represented by the number π. Since πis transcendental it is
impossible to draw a straight line of length πby geometri-
cal construction. Conversely, two lines can be drawn in the
golden ratio, which is often denoted by the Greek symbol phi
whose value is φ=(1 +√5)/2≈1.61803. For example, the
lines of a regular pentagram are subdivided in this ratio.
A right-angled triangle whose shortest sides are unity and
√φhas a hypotenuse of length φ. A cube of side length φhas
faces of area 1+φand volume 1+2φ. The ratio of consecutive
numbers in the Fibonacci series asymptotically converge to
φ. If Fkis the k−th Fibonacci number with F1=F2=1
then φk=Fkφ+Fk−1, even for negative k. The cosine of
π/5 is φ/2. The golden ratio has a simple continued fraction,
φ=1+1/(1 +1/(1 +. . .)), showing it to be irrational and
highly resistant to rational approximation.
Nevertheless, observe that √φ≈14/11. Using π≈22/7
and 22/7=4×11/14 one then finds √φ≈4/π. Consider now
an {11, 14, √112+142=√317}right-angled triangle. By
taking all possible ratios of two sides, three approximations
for πemerge: 22/7, 56/√317 and p176/√317; along with
three approximations for φ: (14/11)2, 317/196 and √317/11.
Of these, the best approximation for πis 22/7 (an overesti-
mate of about 0.040%) whereas the best approximation for φ
is √317/11 (an overestimate of some 0.034%).
One cannot simultaneously reduce both errors by tweak-
ing the triangle’s geometry. The 14:11 ratio (see figure 1) is
almost optimal in the sense of providing two approximations
of comparable quality for πand φ. The two errors would
be exactly equal if a ratio r=[( p1+64φ2/π2−1)/2]1/2≈
2515/1976 ≈14.0005/11 were used instead. The simplest
rational number in the interval (14/11,11r2/14) is 1255/986,
1
a cumbersome and unappealing fraction.
Although an {11, 14, √317}triangle could be marked on
the ground by means of standing stones, Avebury Henge at-
tests to the risk of vandalism. A 3-dimensional design pro-
vides greater resilience against seismic disturbances and ma-
licious attacks. The tetrahedron contains internal right-angled
triangles, but a square-based pyramid allows for alignment
with all four cardinal directions and its geometry affords total
flexibility in the height:base ratio. It is thought the original
design template of the Great pyramid was based on a target
height of 280 cubits and square base of sides 440 cubits which
yields internal triangles in the desired 14:11 ratio.
Normalising the height of the pyramid to unity one finds
results that celebrate π. The base length is 11/7≈π/2 and
the perimeter 44/7≈2π. The distance along an edge from
apex to corner is √438/14 ≈p1+π2/8≈3/2, a reminder
that π≈√10. Each external face has approximately unit
area since 11 √317/196 ≈(π/4) p1+π2/16 ≈1. The total
volume of the pyramid comes to 121/147 ≈π2/12.
Alternatively, normalising the base length to unity show-
cases φ. The height is then 7/11 ≈√φ/2 and the slant length
√317/22 ≈φ/2. The combined area of the triangular faces is
√317/11 ≈φand the total area of the pyramid, including the
base, comes to 1 +√317/11 ≈φ2. In this case, the volume
of the pyramid is 7/33 ≈√φ/6.
By comparing and relating approximations from the inter-
nal {11,14, √317}triangle alone, numerous expressions can
be obtained for φin terms of π, some of which are presented
in table 1, arranged by accuracy. When inverted, they all yield
the same approximation, π≈4/√φ, as imposed by the geom-
etry of the source triangle.
Table 1: Example approximations for φfrom the Great Pyramid
Expression Error
(2 +π2/42)/(1 +π2/42)+0.028%
√42+π2/π +0.059%
1+π2/42-0.073%
2−π4/44+0.090%
4/√42−π2-0.154%
42/π2+0.192%
1/(1 −π4/44) -0.236%
π2(2 +π2/42)/42-0.237%
π2/(42−π2) -0.500%
44/π4−1+0.622%
If the shortest sides of the internal triangles were scaled by
the factor 7π/22 ≈0.9996 then the best existing estimate for
π(i.e. 22/7) would be exact. This would necessitate a modest
increase in slope along the mid-line of each face. Even for
the Great Pyramid, these indentations would only amount to
a concavity of ∼46 mm. The original casing stones of highly
reflective white limestone were loosened by a major earth-
quake in the eastern Mediterranean in 1303. Posing a danger
to bystanders, they were subsequently removed and used in
other buildings. This exposed the core blocks, which can be
seen to exhibit indentations of almost a metre. This has been
known for centuries and is perceptible in some satellite im-
Fig. 1: The Great Pyramid uses simple 11:14 right-angled trian-
gle geometry to simultaneously generate good approximations for
πand the golden ratio φ, outperforming all alternative geometries
less complex than 986:1255, which would be more prone to erosion.
ages – see figure 2. The remains of the original casing stones
seem to be consistent with the pyramid having four flat faces,
though a small yet intentional indentation of the original fin-
ished faces cannot be discounted. The indentations hint that
πcarries most significance whilst alluding to the importance
of the internal right-angled triangles of the pyramid and the
present interpretation that the geometry deliberately and si-
multaneously draws attention to both πand φ.
Ancient Riddles for Modern Times
The alignment of the Great Pyramid to true north required
ingenuity. Its colossal size demanded vast manpower, deter-
mination and natural resources. Although these things are not
entirely beyond the realm of possibility, the geographical po-
sitioning of the Great Pyramid would have required knowl-
edge of a kind the ancient Egyptians could not have cred-
ibly acquired without external input. Previous generations
were fascinated to learn that the Great Pyramid is located
barely a mile south of latitude 30 degrees north, prompting
many to suspect that the ancient Egyptians understood that
the world was round and had methods of estimating latitude.
In this technological age of GPS navigation and the internet,
more accurate data has become readily accessible. Some have
been intrigued to discover that the Great Pyramid’s latitude
matches, to jaw-dropping precision, the value of an extremely
important physical constant – one that history tells us was not
even roughly estimated until the 17th century.
From annual drift in the timing of the eclipses of Jupiter’s
moon Io, Ole Romer deduced in 1676 that light does not
travel at infinite speed. By 1862 Foucault had used a rotat-
ing mirror to measure its speed to an accuracy of 0.6%. The
Michelson-Morley experiment of 1887 subsequently showed
the speed of light, c, to be independent of the Earth’s motion
through space. This curious fact ultimately spurred Einstein
to conceive of relativity, leading him to conclude via E=mc2
2
Fig. 2: The Great Pyramid’s faces are slightly indented, most visible
here as a crease down the mid-line of the right face. The geometry
simultaneously encodes approximations for both πand φ, highlight-
ing various relationships between them. The centre of the pyramid’s
base lies just 11 metres south of the “speed of light latitude”, indi-
cated here by the red dot, and challenging the history of science.
that a little mass is equivalent to a huge energy. The speed
of light was standardised in 1983 to be 299,792,458 m·s−1
by definition. Since then, the S.I. unit of distance has been
derived from cand the S.I. unit of time. If latitudes are ex-
pressed in degrees, they cannot lie outside the range ±90◦, but
ccan be scaled down by shifting the decimal point. Good ge-
ographical resolution is afforded by identifying the speed of
light with the latitude 29.9792458◦or 29◦58’45”. The apex
of the Great Pyramid of Giza is located at this very latitude
north of the equator to an accuracy of about six significant
digits, see figure 2.
Land is present at the same longitude as the Great Pyra-
mid at latitude 30◦S so why might the northern hemisphere
have been selected? Notice that the Earth’s longest geodesic
traversing neither sea nor ocean involves a great circle seg-
ment that does not encroach on the southern hemisphere. The
distance from (6.745N, 11.385W) on the coast of Liberia to
(25.452N, 119.636E) on the Chinese coast opposite Taiwan is
13,642 km, see figure 3. This result is equivalent to more than
one third of the Earth’s circumference. It exceeds by 69 km a
similar suggestion mentioned on Wikipedia’s entry “Extreme
Points of Earth: along any great circle”: (5.048N, 9.123W) to
(28.285,121.638). Giza lies close to both options.
However, there are many possible locations along this
same geodesic and there is scope to alter the latitude since the
values of the physical constants have no intrinsic significance
(unless they happen to be dimensionless). Different defini-
tions of length or time could have influenced the numerical
value of the speed of light.
Logistics would surely have been a paramount consid-
eration when a suitable location for the Great Pyramid was
selected. A plateau near a major river would be preferable,
especially if there is a plentiful supply of easily worked sedi-
mentary limestone nearby. It is known that ships transported
stones and obelisks down the Nile to the Giza plateau during
the erection of the pyramids and nearby temples. The river
also facilitated the arrival of labourers from afar. The arid
Egyptian climate benefits the preservation of limestone struc-
tures which suffer from chemical erosion on exposure to wa-
ter and atmospheric carbon dioxide via the chemical reaction
CaCO3+CO2+H2O→Ca(HCO3)2.
The meridian that traverses most land lies over to the west
of Giza, deep within the Libyan Desert. The lengthiest path
of constant longitude that traverses neither sea nor ocean can
be found at a longitude of ∼99 degrees east. No line of
latitude today completely avoids both the Persian Gulf and
the Mediterranean but that may not have been true when the
Great Sphinx of Giza was constructed.
Many have concluded that the body of the Sphinx, as op-
posed to its disproportionate modern head is several thousand
years older than the Great Pyramid – see figure 5. Pronounced
vertical fissures exist in the enclosure walls of the Sphinx,
consistent with long-term exposure to heavy rainfall during
a much wetter climate predating the pyramids. This supports
Robert Bauval’s postulated correlation between the 45◦orien-
tation of the Giza pyramids and the stars of Orion’s belt dur-
ing their 10,500 BC celestial nadir, when the eastward gaze of
the Sphinx was directed towards the constellation Leo. This
evidence was already persuasive but note that sea levels were
over 100 m lower during the Ice Age, draining the northern
end of the Persian Gulf and opening up a 12734 km path
of constant latitude over land between (29.975N, 9.732W)
near Agadir and (29.975N, 122.326E) near Shanghai. Indeed,
the Sphinx may have been built when sea levels were only
5∼10 m lower, as the Ice Age came to an end (figure 3).
Whilst the congruence between the Great Pyramid’s lati-
tude and the speed of light entirely depends on the definition
of the S.I. units, the positioning of Avebury at latitude 2π/7
radians clearly does not. This naturally implies that the Great
Pyramid’s curious latitude may be no mere coincidence ei-
ther, a conclusion strongly reinforced here by geographical
considerations. To impressive accuracy, Giza is located at the
intersection of the longest great circle path and the longest
constant latitude path traversing neither sea nor ocean (figure
3). Could the S.I. units of length and time have been mas-
saged to ensure that the latitude of the Great Pyramid, when
expressed in degrees, corresponds to the speed of light?
Prior to the accurate measurement of c, which we can
be confident the ancient Egyptians never attempted, the lat-
itude of the Great Pyramid would have seemed unremarkable
except perhaps for its proximity to 30 degrees north. This
covertness was presumably intentional. Might there be some
deliberate obfuscation of the longitude also? Quite possi-
bly. By taking the six most significant digits of π, cyclically
permuting the lowermost three digits, and then cubing the
outcome 3.14591, the result tallies with the longitude of the
entrance to the Great Pyramid, 31.13428◦E. The alternative
π3≈31 could have aroused suspicion too early.
The quantity π/4≈11/14 represents the area of a circle
3
Fig. 3: Giza lies at the intersection of the world’s lengthiest great circle (13642 km) and the world’s lengthiest parallel over land (12734
km), a record set during the last ice age. Conveniently located near the Nile and a plentiful supply of limestone, the Great Pyramid has
experienced little precipitation. In contrast, the Sphinx and its enclosure exhibits considerable erosion, much of it due to heavy rainfall.
divided by the square of its diameter whereas φhas connec-
tions to the algebraic factorisation x2−a2=(x−a)(x+a).
If x=φthen it is possible to write x=(x−1)(x+1).
The Great Pyramid’s geometry draws attention to some inter-
esting mathematical coincidences which all derive from the
14:11 ratio. Although 22/7 is a somewhat crude approxima-
tion for π, inferior to 355/113 in accuracy but not in simplic-
ity, this geometrical arrangement is extremely difficult to im-
prove upon if simultaneous approximations are sought for π
and φ, and one is also interested in learning how the two might
be related. In short, a remarkably sophisticated choice has
been made, without recourse to alternatives far more convo-
luted than the elegant 14:11 ratio. Uglier alternatives such as
2515:1976 could hardly be expected to remain recognisable
after 4500 years of weathering and vandalism.
The ratio of the pyramid’s perimeter to its height is ∼2π,
the combined area of its triangular faces divided by the base
area is ∼φand its total area divided by the base area is ∼φ2.
The approximation φ≈√5π/6 has an error of less than 8
parts per million. Perhaps it does not appear in table 1 be-
cause it has another rˆ
ole. The length of the cubit, ∼523.5 mm,
is accurately known e.g. from the dimensions of the granite-
lined King’s Chamber within the Great Pyramid, a precision
engineered room flaunting knowledge of the Pythagorean the-
orem. Notice that π−φ2≈0.52356 and so one cubit can be
expressed as π−φ2metres. With the Great Pyramid’s geome-
try drawing attention to πand φ, since 6φ2≈5πthe astonish-
ing conjunction π−φ2≈π/6≈φ2/5 clearly pertains to the
cubit and indicates the predestination of the metre.
That is not all. The quantity π−φ2can represent an angle
which accurately approximates the Great Pyramid’s latitude
when converted to radians. Translating this angle (which also
represents the cubit in metres) to degrees yields a good esti-
mate for the speed of light in S.I. units. This cannot be due
to some prank: continental shorelines dictate that Giza lies at
the intersection of two important geographical routes. Much
later, the metre was officially redefined as one ten millionth of
the distance between the north pole and the equator in 1793,
but this had no impact whatever on the cubit, which had al-
ways been related to the size of the Earth. Hence, the scaling
of the Great Pyramid always has deliberately encoded infor-
mation about the Earth’s size and the speed of light.
Notice that the Great Pyramid’s original geometry was
based on a 280:220 cubit triangle. Though the ancient Egyp-
tians used the base ten numbering system, the nearest integer
alternatives, preserving the 14:11 geometry, are 266:209 and
294:231 cubits, changing the overall scale by ∼5%.
Fig. 4: The Great Sphinx guards the pyramids. After prolonged
evolutionary turmoil, what might this ancient chimera signify?
A change of scale by 5% would be disastrous, upsetting
the following facts. Take double the base length, 880 cubits,
and multiply it by the number of seconds in a day to obtain
39807 km. Take the slant length of the pyramid, 20 √317 cu-
bits, and multiply it by the number of seconds in a minute
(or minutes in an hour) and the number of seconds per hour
to obtain 40269 km. Both results provide good estimates of
the Earth’s circumference but their mean, 40042 km, almost
4
perfectly agrees with 40041.4 km, the average of the Earth’s
equatorial circumference and meridional circumference. An
estimate of the Earth’s radius accurate to 0.6% can be had by
multiplying the pyramid’s height by the seconds in 12 hours.
Multiply the height by seconds per hour and then 76, the num-
ber of years in four Metonic cycles (the longest possible sol-
stice solar eclipse season), to derive the Earth’s circumference
again. Furthermore, the Earth’s total mass is ∼1015 times
that of the pyramid and the equator travels a distance approx-
imated by twice the pyramid’s base length each second due
to the Earth’s rotation. Hence, the pyramid’s scaling demon-
strates knowledge of the length of a second, minute and hour,
in addition to the Earth’s size and rotation rate.
Reflections upon the Great Pyramid
One can interpret the Great Pyramid as a sophisticated and
subtle attempt to convince us that advanced intelligence long
ago graced this planet. Its ingenious geometry draws atten-
tion to πand φ, both of which are elegantly related to the
length of the ancient Egyptian cubit in metres. Much as the
Earth’s circumference is πtimes its diameter, the cubit/metre
ratio can be represented by the factors π/6, φ2/5 and π−φ2.
Regarding these remarkably similar quantities as angles, con-
version from radians to degrees using 180/π provides good
estimates for the latitude of the Great Pyramid. The diameter
of Avebury henge, a monument older than the Giza pyramids
yet younger than the Sphinx, provides evidence that the de-
signers anticipated the subdivision of a full rotation into 360
degrees. Multiplying the latitude of the Great Pyramid by ten
million yields 299,792, the speed of light in km·s−1.
The construction of this gargantuan monument was no
frivolous exercise in communicating across a chasm of time,
facts we are already aware of. There are many profound
implications of the findings reported here, which this brief
and necessarily superficial analysis can hardly be expected to
fully address. It is quite plausible that the Great Pyramid ex-
horts us to believe that, with time, effort and patience, there
is hope that even the greatest of mysteries might unravel.
Giza, home of the ancient Sphinx and the world’s tallest
pyramids, lies at the intersection of the longest great circle
traversing neither sea nor ocean with the longest path of con-
stant latitude traversing neither sea nor ocean. The construc-
tion of the Great Sphinx has in all probability commemorated
this since the end of the Ice Age about 12,000 years ago. This
accords with geological evidence and archaeoastronomical
deductions based upon stellar alignments and celestial preces-
sion. Many have long suspected that the advanced weathering
apparent on the Sphinx and its enclosure allude to torrential
rainwater and a harsher climate, pointing to a far older origin
than most Egyptologists are prepared to concede.
The 14 : 11 pyramid geometry disproves notions that the
Greeks invented mathematics some 2,600 years ago. Letting
µ=14/11, the Great Pyramid celebrates πand φby draw-
ing attention to the fact that π≈4/µ ≈4/p1+1/µ2≈
4/4
p1+µ2and φ≈µ2≈1+1/µ2≈p1+µ2from which one
can derive all the approximations of table 1 relating φto π. In-
deed, since φ=(Fkφ+Fk−1)1/k, an infinite tower of further ap-
Fig. 5: The Great Pyramid simultaneously celebrates πand φ, gen-
erating a set of approximations relating the two. The length of the
cubit in metres, π−φ2, exploits a similar approximation, 6φ2≈5π,
thereby serving as the basis for geographical and physical measures.
proximations for φas a function of πcan be generated to arbi-
trary accuracy, the simplest being φ=pφ+1≈p1+16/π2
and φ=3
p2φ+1≈3
p1+32/π2. If there is a desire to avoid
deriving the Fibonacci numbers, Fk, iteration can be used to
refine existing expressions via φj+1=p1+φj.
The latitude of the Great Pyramid accords to one part per
million with the modern value of the speed of light, a physical
quantity our ancient ancestors could not even have estimated,
let alone accurately measured. It also emerges that the metric
length of the cubit represents the speed of light on conversion
from radians to degrees. The three expressions π−φ2,π/6 and
φ2/5 are equivalent to within 0.01%. Not only do they tally
with the cubic:metre ratio and approximate the latitude of the
Great Pyramid, they match (to ∼0.2%) the ratio of the radius
of the Moon’s penumbral shadow to the Earth’s radius dur-
ing a solar eclipse near aphelion and lunar perigee, in other
words during the greatest magnitude solar eclipses. The ab-
solute scaling of the pyramid encodes information pertaining
to the size of the Earth, the length of the second and its rate
of rotation. There can be very little remaining doubt that the
speed of light was very accurately known in antiquity.
The Great Pyramid was not a grandiose tomb for a Pharaoh
preoccupied with his own afterlife. It exploits geometry to
establish relationships between ancient and ‘modern’ units,
allowing the communication of a surprising and important
fact: precise knowledge of the speed of light existed here on
Earth even during the Ice Age. The fact that the pyramids
have an orientation matching that of the Orion constellation
as it appeared when the Sphinx was built is therefore entirely
plausible. With the internal passages of the Great Pyramid
aligned to the meridian, and Polaris closely approaching ce-
lestial north, the dearth of bright pole stars since the con-
struction of the pyramids is finally ending – just as conclusive
evidence has emerged pointing to the existence of advanced
knowledge on Earth in times of antiquity. Before attempt-
ing to further interpret the meaning of these discoveries along
with the findings of a recent, and closely-related analysis of
Avebury Henge, further clues pertaining to a third ancient
monument await scrutiny and analysis.. .
5