Numbers, Ratios and Geometry: Plato and Pythagoras
Much literature exists about how Plato and Pythagoras approached numbers and measurements as can be seen in my post of references. But I will use as my reference here the book written in the 1970's by Morris Kline, a friend of mine from my graduate school years. I used his definitive textbook, Mathematical Thought from Ancient to Modern Times * for a required course that I taught at NYU: " Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty . Mathematics is an art, and as such affords the pleasures which all the arts afford." A newer version exists: Mathematics for the Non-mathematician . Another book by Kline: Mathematics of Certainty. He considered Pythagoreans 'superficial' but they did develop two very important doctrines (pg 15): Nature is built according to mathematical principles. Number relations underly, unify and