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The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?-500 B.C.?), who was perhaps the first to offer a proof of the theorem. But people had noticed the special relationship between the sides of a right triangle long before Pythagoras. [pic] The Pythagorean theorem 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 hypoteneuse, or, in mathematical terms, for the triangle shown at right, a2 + b2 = c2. Integers that satisfy the conditions a2 + b2 = c2 are called "Pythagorean triples." The most famous discovery that Pythagoras made came from his fascination with the Egyptian 3-4-5 rope-stretchers triangle. He had spent years thinking about it and what magic it might hold. Lo and behold, DID hold a great deal of mathematics and for Pythagoras that was the same thing as magical power. One day while drawing in the sand he found that if a square is drawn from each side of the 3-4-5 triangle, the area of the two small squares added together equals the area of the large square. |[pic] |3^2+4^2=5^2 | | |9 + 16 = 25 | He examined other right traingles and found it was true with them also: 6^2 + 8^2 = 10^2 36 + 64 = 100 9^2 + 12^2 = 15^2 81 + 144 = 225 So he decided to announce it as a revelation from the god Apollo, who many claimed to be his father. When he revealed this finding to his followers, he used the general terms of a & b for the shorter legs and c for the longer side which he gave the name "hypotenuse". Thus we have the famous PYTHAGOREAN

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