1. Pythagoras Sheryl Trembley Math 187 11/28/11

2. Pythagoras - philosopher and mathematician Limited reliable information is available about Pythagoras Lived 569 BC – 500 BC (estimated) Born on the Greek isle of Samos Travelled extensively in his youth seeking knowledge

3. The Pythagoreans A society founded by Pythagoras The society followed a code of secrecy It was very mathematical in nature Somewhat religious as well Women were allowed to join the society and were treated as equals

4. Contributions of Pythagoras and the Pythagoreans Contributions were made to fields of mathematics, philosophy, astronomy and music theory Two Major Contributions to Mathematics Established the importance of proofs Discovery and proof that not all numbers are rational Some question whether or not Pythagoras contributed much to mathematics or philosophy

5. Pythagorean Theorem In a right angled triangle, the area of the square of the hypotenuse is equal to the sum of the areas of the squares of the other two sides. That is …. a 2 + b 2 = c 2 The theorem has perhaps more proofs than any other result in mathematics. It is believed that this formula was being used possibly 1000 years prior to Pythagoras by the Indians and Babylonians but he was the first to offer a proof.

6. The Proof c 2 = (area of large square) = (area of triangle) + (area of triangle) + (area of triangle) + (area of triangle) + (area of small square) = ½.ab + ½.ab + ½.ab + ½.ab + (a-b) 2 = 2ab + [a 2 – 2ab + b 2 ] = a 2 + b 2

7. Animated View of the Proof

8. References Steven G. Krantz (2010) The Proof is in the Pudding: The Changing Nature of Mathematical Proof Clifford A. Pickover (2009) The Math Book: Pythagoras to the 57 th Dimension en.wikipedia.org/wiki/Pythagoras www-history.mcs.st- and.ac.uk/Mathematicians/Pythagoras.html www.cut-the-knot.org/pythagoras/index.shtml www.cut-the-knot.org/pythagoras/index.shtml