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In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and ''c'', often called the "Pythagorean equation": : where ''c'' represents the length of the hypotenuse and ''a'' and ''b'' the lengths of the triangle's other two sides. Although it is often argued that knowledge of the theorem predates him,〔 the theorem is named after the ancient Greek mathematician Pythagoras ( 570 – 495 BC) as it is he who, by tradition, is credited with its first recorded proof.〔 According to , Vitruvius says that Pythagoras first discovered the triangle (3,4,5); the fact that the latter is right-angled led to the theorem.〕 There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework.〔. For a different view, see , where the speculation is made that the first column of tablet 322 in the Plimpton collection supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by ((pdf file )). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also §2, page 7.〕 Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases. The theorem has been given numerous proofspossibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but ''n''-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound. ==Pythagorean proof== The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it.〔Posamentier, Alfred. ''(The Pythagorean Theorem: The Story of Its Power and Beauty )'', p. 23 (Prometheus Books 2010).〕 In any event, the proof attributed to him is very simple, and is called a proof by rearrangement. The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem, Q.E.D.〔Benson, Donald. ''(The Moment of Proof : Mathematical Epiphanies )'', pp. 172–173 (Oxford University Press, 1999).〕 That Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus.〔Maor, Eli. ''(The Pythagorean Theorem: A 4,000-year History )'', p. 61 (Princeton University Press, 2007).〕 Several other proofs of this theorem are described below, but this is known as the Pythagorean one. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pythagorean theorem」の詳細全文を読む スポンサード リンク
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