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Xuan tu or Hsuan thu (simplified Chinese: 弦图; traditional Chinese: 絃圖; pinyin: xuántú; Wade–Giles: hsüan 2 tʻu 2) is a diagram given in the ancient Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. [1]
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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
The theorem for which the greatest number of different proofs have been discovered is possibly the Pythagorean theorem, with hundreds of proofs being published up to date. [3] Another theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss alone had eight different proofs of ...
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.
Brauer–Suzuki–Wall theorem (group theory) Brauer's theorem (number theory) Brauer's theorem on induced characters (representation theory of finite groups) Brauer's three main theorems (finite groups) Brauer–Cartan–Hua theorem (ring theory) Bregman–Minc inequality (discrete mathematics) Brianchon's 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.
Liouville's theorem (complex analysis) Markov's inequality (proof of a generalization) Mean value theorem; Multivariate normal distribution (to do) Holomorphic functions are analytic; Pythagorean theorem; Quadratic equation; Quotient rule; Ramsey's theorem; Rao–Blackwell theorem; Rice's theorem; Rolle's theorem; Splitting lemma; squeeze ...