“
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 Platonic solids: the equilateral triangle... the square... and the re
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― "GOLDEN" NON-EUCLIDEAN GEOMETRY, THE: HILBERT'S FOURTH PROBLEM, "GOLDEN" DYNAMICAL SYSTEMS, AND THE FINE-STRUCTURE CONSTANT
― "GOLDEN" NON-EUCLIDEAN GEOMETRY, THE: HILBERT'S FOURTH PROBLEM, "GOLDEN" DYNAMICAL SYSTEMS, AND THE FINE-STRUCTURE CONSTANT
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Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
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― A Mathematician's Apology
― A Mathematician's Apology
