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Pythagoras

Pythagoras. Sheryl Trembley Math 187 11/28/11. 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. The Pythagoreans.

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Pythagoras

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  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. • Thatis …. a2 + b2 = c2 • The theorem has perhaps more proofsthananyotherresult in mathematics. • It isbelievedthatthis formula wasbeingusedpossibly 1000 yearsprior to Pythagoras by the Indians and Babylonians but hewas the first to offer a proof.

  6. The Proof • c2 = (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 + [a2 – 2ab + b2] • = a2+ b2 ⧅

  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 57th Dimension • en.wikipedia.org/wiki/Pythagoras • www-history.mcs.st-and.ac.uk/Mathematicians/Pythagoras.html • www.cut-the-knot.org/pythagoras/index.shtml

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