Maths History Club

Pythagoras of Samos is most famously credited for discovering the theorem relating the three sides of a right angled triangle (though evidence suggests that this theorem was not discovered by Pythagoras and was actually in use in many parts of the world before Pythagoras’s birth). However, few know about the Pythagorean Brotherhood - a cult formed by Pythagoras in Croton in Southern Italy in the 5 th Century BC that lasted almost 200 years after his death. Though the Pythagoreans shared many ritualistic features with other cults such as wearing robes, observing sexual purity, maintaining utmost secrecy and loyalty, and not touching beans, it was unique in its worship of numbers and their metaphysical. Pythagoreans believed in the metaphysics of number and that reality was mathematical in nature. They also believed that spiritual purity could be achieved through the study of philosophy and mathematics. ALL IS NUMBER - Pythagorean Motto Pythagoreans believed in the concept of tetraktys,

You may be familiar with Pythagoras’ Theorem. This simple yet significant theorem is a staple in secondary education around the world and oftentimes your best friend when it comes to geometry problems. This simple theorem is backed up with many simple and elegant proofs easily understandable by anyone who can understand the theorem itself. This is exemplified by this rearrangement proof: See how the the yellow areas in the first diagram can be rearranged to form the second diagram and how this proves Pythagoras’ Theorem. Now, there are some integers that satisfy Pythagoras’ Theorem. These are referred to as Pythagorean Triples and there is an infinite amount of them (Why?). Some small examples include (3,4,5), (5,12,13) and (8,15,17).   Finding Pythagorean Triples is an example of solving a Diophantine equation – equations which have positive integer solutions for all variables. Unsurprisingly, Diophantine equations are named after Diophantus who developed methods for solving such equa