By Emily Bennett 12 The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras. (approximately 500 B.C.) Pythagoras himself.

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Presentation transcript:

By Emily Bennett

12 The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras. (approximately 500 B.C.) Pythagoras himself was not simply a mathematician. He was an important philosopher who believed that the world was ruled by harmony and that numerical relationships could best express this harmony. He was the first to represent musical harmonies as simple ratios.

34 Pythagoras and his followers were also a bit peculiar. Pythagoras's followers were sworn to absolute secrecy, and their devotion to their master bordered on the cult-like. Pythagoreans followed a strict moral and ethical code, which included vegetarianism because of their belief in the reincarnation of souls. The Pythagorean theorem is arguably his most influential theorem. It states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypotenuse. In mathematical symbols a 2 + b 2 = c 2.

56 People had noticed the special relationship between the sides of a right triangle long before Pythagoras Ancient clay tablets from Babylonia These tablets indicate that the Babylonians, a thousand years before Pythagoras, has rules for generating Pythagorean triples, understood the relationship between the sides of a right triangle, and, in solving for the hypotenuse of an isosceles right triangle, came up with an approximation for the square root of two, accurate to five decimal places.

78 We do not know for sure how Pythagoras himself proved the theorem that bears his name because he refused to allow his teachings to be recorded in writing. One geometric proof demonstrations that the combined areas of squares with sides of length a and b will equal the area of a square with sides of length c, where a, b, and c represent the lengths of the two sides and hypotenuse of a right triangle

910 Many other proofs exist today that follow a geometric or algebraic line of reasoning. We may not know much about Pythagoras, but we do know is that his work has had a profound effect on mathematics! There are many applications of the Pythagorean theorem. It can be used to find the distance between two cities using a reference point or the magnitude of a vector given its horizontal and vertical components.

1112 Sources: All pictures come from Google Images or clip art and are free to use for the public. Knierim, Thomas. Mathematical Association of America. "Ivar Peterson's Math Trek: Square of the Hypotenuse." Pythagoras andrews.ac.uk/history/PictDisplay/Pythagoras.html andrews.ac.uk/history/PictDisplay/Pythagoras.html