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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 Thomsen's theorem ： ウィキペディア英語版 Thomsen's theorem Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point. Consider an arbitrary triangle ''ABC'' with a point ''P''1 on its edge ''BC''. A sequence of points and parallel lines is constructed as follows. The parallel line to ''AC'' through ''P''1 intersects ''AB'' in ''P''2 and the parallel line to BC through ''P''2 intersects AC in ''P''3. Continuing in this fashion the parallel line to AB through ''P''3 intersects BC in ''P''4 and the parallel line to ''AC'' through ''P''4 intersects ''AB'' in ''P''5. Finally the parallel line to ''BC'' through ''P''5 intersects AC in ''P''6 and the parallel line to ''AB'' through ''P''6 intersects ''BC'' in ''P''7. Thomsen's theorem now states that ''P''7 is identical to ''P''1 and hence the construction always leads to a closed path ''P''1''P''2''P''3''P''4''P''5''P''6''P''1 ==References== *''Satz von Thomsen'' In: ''Schülerduden – Mathematik II''. Bibliographisches Institut & F. A. Brockhaus, 2004, ISBN 3-411-04275-3, pp. 358–359 (German) 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「Thomsen'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.