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Figure This!

Pythagoras was a Greek mathematician (about 580–500 BC) who formed a secret society based partly on mathematical discoveries. The motto of his followers is said to have been "All is number."

What is called the Pythagorean Theorem was known to the Egyptians as early as 2000 BC and to the Babylonians in 1700 BC.

The Hindu mathematician Bhaskara (about 1114-1185) proved the Pythagorean Theorem simply by drawing this picture and saying “Behold!”


Lewis Carroll, author of Alice in Wonderland, and US President James Garfield wrote proofs of the Pythagorean Theorem.

French mathematician Pierre Fermat (1601–1665) built on the Pythagorean Theorem by proving that no cube is the sum of two cubes and no fourth power is the sum of two fourth powers. He believed that the same was true for all whole-number powers greater than 2. He wrote in the margin of a notebook that he had a proof of his belief, but the margin was too small for the proof. Only in 1995, more than 300 years later, did British-born mathematician Andrew Wiles find the key that proved Fermat correct.

Choose any two different positive counting numbers a and b with a the bigger of the two. If

  • x = 2ab,

  • y = a2 - b2, and

  • z = a2 + b2;

then x, y, and z form a Pythagorean triple.




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