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Mathematics in archeological artifacts and structures

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Project log

Dimitrios S. Dendrinos
added a research item
The paper’s objective is to discuss and critically analyze the papyrus fragment P. OXY. 29 that contains what is considered to be Proposition 5, from Book II, of Euclid’s Elements. This particular fragment contains enough information on it to draw some preliminary conclusions regarding its making. It is suggested that P. OXY. 29 contains a scribe’s personal drawing, inserted at some later date than when the text was written. Hence, it is inferred that possibly two different scribes are involved in the making of this artifact; or the same scribe writing on the papyrus at two different points in time, relatively within close temporal proximity. The text of course was not directly copied from the original Euclid text, which was very likely written in capital (uppercase) Greek letters, but rather from a prior copy (or the end point from a series of multiple copies) of the original and after the transition from Greek koine to a proto-Byzantine lowercase cum uppercase writing. Analysis of the fragment’s context, form, as well as its content, and especially what is omitted from the diagram as drawn that also provides clues as to its dating, are attempted. The spatial-temporal paths of both fragment and content are sketched out. It is suggested that the writing took place, possibly, slightly later than the currently prevailing view, which holds that the artifact was made in the 75 – 125 AD time frame.
Dimitrios S. Dendrinos
added 2 research items
This is the second paper in a series of two papers on ancient artifacts movement in space-time. The paper presents the theoretical mathematical model, which is an extension of the Universal Map of Discrete Relative Spatial Dynamics developed by D. Dendrinos and M. Sonis in the 1980s. The paper expands on this model and offers a comprehensive approach to both population stocks and artifacts' accumulations and flows in space-time.
This is the first paper of a two-paper series, dealing with ancient artifacts and their movement in space-time. It provides the background to the theoretical mathematical model supplied in the second paper.
Dimitrios S. Dendrinos
added 29 research items
This is review of the 1941 classical book by Oscar Broneer about the Amphipolis Lion. It critically appraises the contribution made by the author of the book in recording the thought processes involved in both the Lion's reconstruction, as well as the efforts towards producing a proposed conjectured restoration. In evaluating the book, the author documents three propositions: the monument was not assembled in antiquity; the monument could not stand as conjectured; and that this is the reason why it was abandoned. The reviewer documents also that the Lion was reconstructed in situ, where it was intended to be raised by its original makers at the closing decades of the 4th Century BC. Further, the reviewer revises some of his prior suggestions about the intended location of the monument.
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 academia.edu here: https://www.academia.edu/31671102/ON_THE_FUZZY_NATURE_OF_SHADOWS and also here at researchgate.net here: https://www.researchgate.net/publication/317506046_On_the_Monoliths'_Shadows
This is an update of the same paper by the same author. It contains a photo of Kerbstone K51 and corrects an error from the previous two versions of the paper, which had a photo of Dowth South's Entrance instead of Dowth North's Entrance as a cover photo. I wish to thank Michael Fox for pointing that out to me.
Dimitrios S. Dendrinos
added a research item
A new class of ellipses is discussed in this paper, with the bezel ellipse of the Minoan 5-priestess signet ring from the 1450 BC Pylos’ tomb of the Mycenaean Griffin Warrior acting as the springboard to this new classification. The ellipse carries a strong mathematical interest. The elementary theorems governing ellipses that obey the condition that the ratio of their major to minor axes is at a Golden Ratio are stated, and to that end nine sets of mathematical theorems are proven. Following the mathematical exposition of the Golden Ratio Ellipse, the ring from Pylos is examined as to whether its maker was aware of any of these Mathematics. It is concluded that although, and on purely Aesthetics grounds, the maker gravitated and tried to approximate the making of a true Golden Ratio Ellipse, (s)he was only partially aware of the underlying Mathematics. The findings are based on a detailed analysis of the ring’s iconography