"In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the s: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the ... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the ... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
, Samuil Aranson, The “Golden” Non-Euclidean Geometry: Hilbert's Fourth Problem, “Golden” Dynamical Systems, and the Fine-Structure Constant (2016)
https://en.wikiquote.org/wiki/Mathematics_and_mysticism
Revision History
No revisions have been submitted for this quote.
Categories
Mathematics and mysticism
61 quotes on TrueQuotesView all quotes by Mathematics and mysticism →
Related Quotes
"Of the perfection of the number six, which it the first of the numbers which is composed of its aliquot parts. These …"
"What English mathematicians were most intrigued by and, at times, embarrassed about was the explanation Ramanujan off…"
"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mat…"
"Throughout history philosophers and mystics have sought a compact key to universal wisdom, a finite formula or text w…"
"The Pythagorean mathematical concepts, abstracted from sense impressions of nature, were... projected into nature and…"
"Number mysticism was not original with the Pythagoreans. The number seven, for example, had been singled out for spec…"
"When a man counts one, two, three, he is not only doing mathematics, he is on the path to the mysticism of numbers in…"
"Figuration can be one of the values or qualities that the Divine Artificer uses to decorate or adorn the invisible fi…"
"At Babylon... we see a practical polytheism... combined with the application of the exact sciences, and the gods of h…"
"Now this ratio of the single to the double arises, no doubt, from the ternary number, since one added to two makes th…"