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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.
IM 67118, also known as Db 2-146, is an Old Babylonian clay tablet in the collection of the Iraq Museum that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal. In the last part of the text, the solution is proved correct using the Pythagorean theorem. The steps of the solution are believed ...
By the Pythagorean theorem we have b 2 = h 2 + d 2 and a 2 = h 2 + (c − d) 2 according to the figure at the right. Subtracting these yields a 2 − b 2 = c 2 − 2cd. This equation allows us to express d in terms of the sides of the triangle: = + +. For the height of the triangle we have that h 2 = b 2 − d 2.
Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.
Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem discovered by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876).
English: Construction by New Orleans students Calcea Johnson and Ne’Kiya Jackson that yields a trigonometric proof of the Pythagorean theorem for a<b. [1] The proof is valid for almost all right triangles, except for the case when a=b, i.e. Isosceles Right Triangle.