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Pythagorean Theorem

Math project on the pythagorean theorem

Grace Paulson

on 17 April 2013

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Transcript of Pythagorean Theorem

By: Grace Paulson The Pythagorean Theorem Pythagoras More about Pythagoras Jobs Ancient History Websites - Who invented/discovered the Pythagorean Theorem is in a dispute while some say that it was discovered by Pythagoras while others point the an indian mathematician Baudhayana. However you look at it Pythagoras is the one who proved it.
- We do not know how Pythagoras proofed his theory because he refused to have is teachings or wards to be recorded. - Clay tablets from the ancient Babylonians suggest that in the second millennium the Babylonias had their own rules for creating Pythagorean Triples.
- The ancient Indians used the Pythagorean's Theorem in the context of strict requirements for the orientation, shape, and area of their religious alters. A carpenter uses the Pythagorean theorem to make sure that the structure they are building is square. The product they get out of it is whatever the carpenter was/is building. http://ualr.edu/lasmoller/pythag.html


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"Pythagorean Theorem and its many proofs." What is the Pythagorean Theorem? - The Pythagorean Theorem states that if you have a right angle triangle and there is a square on each side then the area of the two smaller squares will add to the area of the bigger square.
- All Pythagorean's are triples because they consist of three parts (the three sides or three squares) Pythagoras was a mathematician and an important philosopher. He believed that harmony ruled the world and numerical relationships best expressed this harmony. For example he was the first to represent musical harmonies as simple ratios. All Pythagoras's followers where sworn to absolute secrecy and their devotion to him was borderline cult like. They followed a strict ethical code witch included being a vegetarian because of the belief of reincarnation. They also didn't eat beans. "Playing with the applet that demonstrates the Euclid's proof (#7), I have discovered another one which, although ugly, serves the purpose nonetheless.

Thus starting with the triangle 1 we add three more in the way suggested in proof #7: similar and similarly described triangles 2, 3, and 4. Deriving a couple of ratios as was done in proof #6 we arrive at the side lengths as depicted on the diagram. Now, it's possible to look at the final shape in two ways:

as a union of the rectangle (1 + 3 + 4) and the triangle 2, or
as a union of the rectangle (1 + 2) and two triangles 3 and 4.
Equating the areas leads to

ab/c · (a² + b²)/c + ab/2 = ab + (ab/c · a²/c + ab/c · b²/c)/2

Simplifying we get

ab/c · (a² + b²)/c/2 = ab/2, or (a² + b²)/c² = 1
(Pythagorean Theorem 1). cut-the-knot. N.p.. Web. 7 Apr 2013. <http://www.cut-the-knot.org/pythagoras/>. The End
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