Abstract
JUST as the sequence of propositions arranged by Euclid to form the first book of his “Elements” reaches its climax in the proof of Pythagoras's theorem, so those in the three succeeding books culminate in the construction of a regular pentagon. In the eyes of the Pythagorean school of Greek mathematics, the five regular solids were considered to be symbols of perfection. So one of the aims of the first four books of the “Elements” was to supply accepted reasoning that would lead to the construction of regular polygons of three, four, and five sides—the only ones which can be the faces of a regular solid.
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References
"The Scientific Construction of the Regular Heptagon with Angles Correct to Ten Seconds, derived from Two Crossed-Parallelograms of a Semi-Ellipse." By T. Alexander.
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B., W. The Construction of Regular Polygons1. Nature 117, 466–467 (1926). https://doi.org/10.1038/117466b0
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DOI: https://doi.org/10.1038/117466b0