The Pythagorean TheoremThe Pythagorean theorem, or Pythagoras's theorem was know by the Babylonians in 2000 B.C  about 1500 years before the time of Pythagoras.
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This is a very simple and yet powerful theorem, which we can apply to many areas of life. The proofs of this theorem are a little more complicated. Perhaps the simplest is the geometrical proof, given about 1150 by the Indian mathematician Bhaskara  this is illustrated in the videos (right). 

PythagorasPythagoras (569500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cultlike in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.
Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen. Although he is credited with the discovery of the famous theorem, it is not possible to tell if Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. Unfortunately, this vow of secrecy prevented an important mathematical idea from being made public. The Pythagoreans had discovered irrational numbers! If we take an isosceles right triangle with legs of measure 1, the hypotenuse will measure sqrt 2. But this number cannot be expressed as a length that can be measured with a ruler divided into fractional parts, and that deeply disturbed the Pythagoreans, who believed that "All is number." They called these numbers "alogon," which means "unutterable." So shocked were the Pythagoreans by these numbers, they put to death a member who dared to mention their existence to the public. It would be 200 years later that the Greek mathematician Eudoxus developed a way to deal with these unutterable numbers. 

Garfield's Proof 

Origami Proof 


