Pythagorean and Platonian mathematics (Q2707661)

The author discusses the mathematical background of some Platonian writings, intending to reconstruct it in an elementary way using only ideas (essentially) available to Plato. NEWLINENEWLINENEWLINEStarting from the Euclidean algorithm and relative prime number pairs, he moves on to prime numbers. Then he discusses triangular numbers and polygonal numbers more generally, and takes a look at their applications e.g. to a proof of the irrationality of \( \sqrt 2 \), and to some Diophantine equations. NEWLINENEWLINENEWLINELater he considers sections of a line, and the philosophical method of division together with their arithmetical counterparts.