Please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.[Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.]

~ Farkas Bolyai

Farkas Bolyai Bolyai Euclid Euclid S Postulate Fear Happiness Health Intercourse Janos Bolyai Janos Bolyai Lewd Math Mathematics Passion Science Time

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.

~ Euclid

Euclid Euclid Euclidean Geometry Geometry Golden Ratio History Of Mathematics Mathematics Science

Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.[Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.]

~ Farkas Bolyai

Farkas Bolyai Bolyai Euclid Euclid S Postulate Happiness Health Intercourse Janos Bolyai Joy Janos Bolyai Lewd Math Mathematics Measure Parallels Science

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.

~ G.h. Hardy

G.h. Hardy Euclid Gambit Math Mathematics Reductio Ad Absurdum Risk Science Strategy Weapons

I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

~ Alain Badiou

Alain Badiou Badiou Communism Euclid Geometry Mao Maoism Mathematics Party

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 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 golden ratio... (Proposition II.11)... By using the golden isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.

~ Alexey Stakhov

Alexey Stakhov Euclid Geometry Golden Ratio Harmony Plato Platonic Solids