Pythagoras Pythagoras was a Greek scholar and philosopher in the late century BC. Known as “the father of numbers, his teachings covered a variety of areas.

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Presentation transcript:

Pythagoras Pythagoras was a Greek scholar and philosopher in the late century 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.

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

a b c a b c c c a a b 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 + 2ab + b 2 2 Area of each triangle = ab 2 Area of all four triangles = 4ab 2 Area of small square = c 2 Area of everything = 4ab + c 2 2 Therefore, Area of everything = Area of large square 4ab + c = a + 2ab + b ab + c = a + 2ab + b 22 2 c = a + b a+b

 Now we can use GSP software to illustrate that the Pythagorean Theorem will work with ANY similar shapes!