PythagorasSheryl Trembley

Math 18711/28/11

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

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

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

Pythagorean TheoremIn 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 …. a2 + b2 = c2

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.

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 ⧅

Animated View of the Proof

ReferencesSteven 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