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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 Viviani's theorem ： ウィキペディア英語版 Viviani's theorem Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from ''any'' interior point to the sides of an equilateral triangle equals the length of the triangle's altitude. ==Proof== This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is ''h'' and whose side is ''a''. Let P be any point inside the triangle, and ''u, s, t'' the distances of P from the sides. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. Now, the areas of these triangles are $\backslash frac$, $\backslash frac$, and $\backslash frac$. They exactly fill the enclosing triangle, so the sum of these areas is equal to the area of the enclosing triangle. So we can write: :$\backslash frac\; +\; \backslash frac\; +\; \backslash frac\; =\; \backslash frac$ and thus :''u + s + t = h.'' Q.E.D. 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「Viviani's theorem」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.