# Pythagorean theorem

The Pythagorean Theorem

Outline

Introduction

I . The History of the Pythagorean Theorem

II . Some proofs of the Pythagorean Theorem

III . Evolution of the Pythagorean Theorem

IV . Metaphysics and the Pythagorean Theorem

V . How the Pythagorean Theorem Shows Up In Daily Life

Introduction

a2 b2 c2 where a and b are the sides of a right triangle and c is the hypotenuse is the answer most students will give when asked to define the Pythagorean Theorem . Ask them to prove it and most can 't unless they are fairly

advanced in mathematics . By and large , most anyone who has taken high school algebra has encountered this theorem without every really understanding it

In words , the Pythagorean Theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides

The Egyptians , Babylonians and Chinese knew of the right triangle long before Pythagoras came along , and the Egyptians had devised a right triangle of rope with twelve evenly spaced knots for measurements . They knew that 3 , 4 and 5 make a 90 degree angle and used the triangle of rope as an instrument of measurement

This will explore several aspects of the Pythagorean Theorem from its history to how it found in art , how it relates to music and how it occurs in everyday life , whether people know it or not I . The History Of the Pythagorean Theorem

It is not conclusively known that Pythagoras can be solely credited with his famous theorem , but it is known that he was the first to prove why a right triangle behaves the way it does

Born in Samos (now in Turkey ) in about 582 B .C , Pythagoras came from a humble family . Various scenarios of his early life put him in Egypt Babylonia , and Italy , where he founded his school that survived for a few hundred years

Pythagoras was not interested in solving mathematical problems he focused on pure mathematics and geometric relationships

Pythagoras and his Brotherhood (the Pythagoreans ) traveled fairly extensively , and it is known that they visited and studied in Egypt . The Pythagoreans were a mystical group , and Pythagoras himself identified numbers with mysticism

It is possible that Pythagoras saw the knotted triangle in Egypt and went about assigning a numerical value to the geometry of the triangle Nothing of his was written down , though , and while the theorem is attributed to him it could well have been one of his brethren or students that invented the theorem since all in the Pythagorean school was community property , and since his name was the name of the school we have come to know the famous theorem as it is today

How do we know that they Pythagorean Theorem was known before Pythagoras ? So far , nothing has been shown in terms of an equation in relation to a right triangle before Pythagoras , but the right triangle was certainly known for its special properties , as can be seen in...