h of the third side of a right triangle when only knowing the length of two sides. This is considered his most important contribution to math. Pythagoras also invented the five regular solids. It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he knew how to construct the other two. Pythagoras also founded a philosophical and religious school in Croton (now Crotone, on the east of the heal of southern Italy) that had many followers. Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. The beliefs that Pythagoras held were:(1) At its deepest level, reality is mathematical in nature,(2) Philosophy can be used for spiritual purification,(3) The soul can rise to union with the divine,(4) Certain symbols have a mystical significance, and(5) All brothers of the order should observe strict loyalty and secrecy. This society defined figurate numbers to be the number of dots in certain geometrical configurations (Mathematical Structures for Computer Science, Pg. 145).Of Pythagoras's actual work nothing is known. His school practiced secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers. Certainly his school made outstanding contributions to mathematics, and it is possible to be fairly certain about some of Pythagoras's mathematical contributions. Pythagoras's accomplishments have changed the math world tremendously and his contributions to the math world are truly incredible. ...
