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English: Illustration of the Pythagorean theorem. The sum of two squares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple). The sum of two squares whose sides are the two legs (blue and red) is equal to the area of the square whose side is the hypotenuse (purple).
2008-05-20T00:47:20Z Jokes Free4Me 500x540 (13967 Bytes) {{Information |Description=Illustration to Euclid's proof of the Pythagorean theorem, including less important labels and lines. |Source=[[:Image:Illustration to Euclid's proof of the Pythagorean theorem.svg]] |Date=May 20, 2; Uploaded with derivativeFX
Date/Time Thumbnail Dimensions User Comment; current: 20:44, 19 December 2006: 500 × 540 (6 KB): Gerbrant: Changed PQR to ABC, in line with the article (and Euclid, although he uses Greek letters of course).
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
The Bride's chair proof of the Pythagorean theorem, that is, the proof of the Pythagorean theorem based on the Bride's Chair diagram, is given below. The proof has been severely criticized by the German philosopher Arthur Schopenhauer as being unnecessarily complicated, with construction lines drawn here and there and a long line of deductive ...
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
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