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Rearrangement proof of the Pythagorean theorem. (The area of the white space remains constant throughout the translation rearrangement of the triangles. At all moments in time, the area is always c². And likewise, at all moments in time, the area is always a²+b².)
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 steps. According to Schopenhauer, the proof is a "brilliant piece of perversity". [6] The basic idea of the Bride's Chair proof of the Pythagorean theorem
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.
Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.
The observation that subtracting 2A from c 2 yields (b − a) 2 need only be augmented by a geometric rearrangement of areas corresponding to a 2, b 2, and −2A = −2ab to obtain rearrangement proof of the rule, one which is well known in modern times and which is also suggested in the third century CE in Zhao Shuang's commentary on the ...
The Pythagorean theorem is a mathematical puzzle involving three sides of a right triangle. Johnson and Jackson spent months working to solve it using trigonometry, which had never been done before.
The Zhoubi Suanjing, also known by many other names, is an ancient Chinese astronomical and mathematical work.The Zhoubi is most famous for its presentation of Chinese cosmology and a form of the Pythagorean theorem.
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).