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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Steiner inellipse ： ウィキペディア英語版 Steiner inellipse In geometry, the Steiner inellipse,〔Weisstein, E. "Steiner Inellipse" — From MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/SteinerInellipse.html.〕 midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent to the sides at their midpoints. It is an example of an inconic. By comparison the inscribed circle and Mandart inellipse of a triangle are other inconics that are tangent to the sides, but not at the midpoints unless the triangle is equilateral. The Steiner inellipse is attributed by Dörrie〔H. Dörrie, ''100 Great Problems of Elementary Mathematics, Their History and Solution'' (trans. D. Antin), Dover, New York, 1965, problem 98.〕 to Jakob Steiner, and a proof of its uniqueness is given by Kalman.〔.〕 The Steiner inellipse contrasts with the Steiner circumellipse, also called simply the Steiner ellipse, which is the unique ellipse that touches a given triangle at its vertices and whose center is the triangle's centroid. ==Trilinear equation== The equation of the Steiner inellipse in trilinear coordinates for a triangle with side lengths ''a, b, c'' is〔 :$a^2x^2+b^2y^2+c^2z^2-2abxy-2bcyz-2cazx\; =\; 0$ 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「Steiner inellipse」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.