For proper viewing use Macromedia Flash Plug-in version 8 and better. Download a new plug-in, if your system is not playing correctly.

Pythagorean Therom

BY: Cindy Sandra Keila

The equation: a2 + b2 = c2.

REAL WORLD PROBLEM: You've just picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out? You need to throw the ball 127.3 feet to get it from first base to third base.

PROOF: The square described upon the hypotenuse of a right-angled triangle is equal to the sum of the squares described upon the other two sides. Another way of saying the same thing is: When the two shorter sides in a right triangle are squared and then added, the sum equals the square of the longest side or hypotenuse.

History of Pathagoras

He was born in acient greece He was belived to be born in 570 BC Pythagoras' father's name was Mnesarchus and may have been a Phoenician. His mother's name was Pythais. Mnesarchus made sure that his son would get the best possible education. His first teacher was Pherecydes, and Pythagoras stayed in touch with him until Pherecydes' death. When Pythagoras was about 18 years old he went to the island of Lesbos where he worked and learned from Anaximander, an astronomer and philosopher, and Thales of Miletus, a very wise philosopher and mathematician. At some point Pythagoras was exiled from Croton and had to move to Tarentum. After 16 years he had to move again, this time to Metapontus where he lived four years before he died at the age of 99. Now let's talk a bit about the theorem that bears his name. The Egyptians knew that a triangle with sides 3, 4, and 5 make a 90o angle. As a matter of fact, they had a rope with 12 evenly spaced knots that they used to build perfect corners in their buildings and pyramids. It is believed that they only knew about the 3, 4, 5 triangle and not the general theorem that applies to all right triangles. The Chinese also knew this theorem. It is attributed to Tschou-Gun who lived in 1100 BC. He knew the characteristics of the right angle. The theorem was also known to the Caldeans and the Babylonians more than a thousand years before Pythagoras. A clay tablet of Babylonian origin was found with the following inscription: "4 is the length and 5 the diagonal. What is the breadth?" So why is it called the Pythagorean Theorem? Even though the theorem was known long before his time, Pythagoras certainly generalized it and made it popular. It was Pythagoras who is attributed with its first geometrical demonstration. That is why it is known as the Pythagorean Theorem. There are hundreds of purely geometric demonstrations as well as an unlimited (that is right -- an infinite number) of algebraic proofs.