Pythagoras Pythagoras was a Greek scholar and philosopher ca 548 BC to 495 BC. Known as “the father of numbers, his teachings covered a variety of areas.

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Pythagoras Pythagoras was a Greek scholar and philosopher ca 548 BC to 495 BC. Known as “the father of numbers, his teachings covered a variety of areas such as mathematics, music, astronomy, and topography. Born in Samos, he is best known for the Pythagorean Theorem which bears his name.

c b a The Theorem states: Given a right triangle with leg lengths a, b, and hypotenuse length c Hypotenuse c 2 The area of the square whose side length is the hypotenuse (c)… c b 2 b Leg a Is equal to the sum of the areas of the squares whose side lengths are the legs (a) and (b). a 2 Leg In other words:

One such proof is to create a square with side lengths a+b. Although he did not discover the Theorem, he was the first to prove it. One such proof is to create a square with side lengths a+b. Area of large square = (a+b) 2 a b = a + 2ab + b 2 a b c c Area of each triangle = ab 2 a+b Area of all four triangles = 4ab 2 c c b a Area of small square = c 2 b a Area of everything = 4ab + c 2 Therefore, Area of everything = Area of large square 2 4ab + c = a + 2ab + b 2 1 2ab + c = a + 2ab + b 2 c = a + b 2