翻訳と辞書 Words near each other ・ Belt filter ・ Belt friction ・ Belt grinding ・ Belt hook ・ Belt Junction, Texas ・ Belt Line (DART station) ・ Belt Line Road (Texas) ・ Belt lipectomy ・ Belt machine ・ Belt manlift ・ Belt Mathai ・ Belt of the Celts ・ Belt of Venus ・ Belt Parkway ・ Belt press ・ Belt problem ・ Belt Pulley ・ Belt Railway of Chattanooga ・ Belt Railway of Chicago ・ Belt sander ・ Belt Subdivision ・ Belt Supergroup ・ Belt transect ・ Belt Up Theatre ・ Belt Woods ・ Belt wrestling ・ Belt wrestling at the 2009 Asian Indoor Games ・ Belt wrestling at the 2013 Summer Universiade ・ Belt, Montana ・ Belt, North Holland Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Belt problem ： ウィキペディア英語版 Belt problem The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius ''r''1 and ''r''2 whose centers are separated by a distance ''P''. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent angles. == Solution == Clearly triangles ACO and ADO are congruent right angled triangles, as are triangles BEO and BFO. In addition, triangles ACO and BEO are similar. Therefore angles CAO, DAO, EBO and FBO are all equal. Denoting this angle by $\backslash varphi$, the length of the belt is :$CO\; +\; DO\; +\; EO\; +\; FO\; +\; \backslash text\; CD\; +\; \backslash text\; EF\; \backslash ,\backslash !$ :$=2r\_1\backslash tan(\backslash varphi)\; +\; 2r\_2\backslash tan(\backslash varphi)\; +\; (2\backslash pi-2\backslash varphi)r\_1\; +\; (2\backslash pi-2\backslash varphi)r\_2\; \backslash ,\backslash !$ :$=2(r\_1+r\_2)(\backslash tan(\backslash varphi)\; +\; \backslash pi-\; \backslash varphi)\; \backslash ,\backslash !$ This uses the fact that the length of an arc = the radius × the measure of the angle facing the arc in radians. To find $\backslash varphi$ we see from the similarity of triangles ACO and BEO that :$\backslash frac\; =\; \backslash frac\; \backslash ,\backslash !$ :$\backslash Rightarrow\; \backslash frac\; =\; \backslash frac\; \backslash ,\backslash !$ :$\backslash Rightarrow\; \backslash frac\; =\; \backslash frac\; \backslash ,\backslash !$ :$\backslash Rightarrow\; =\; \backslash frac\; \backslash ,\backslash !$ :$\backslash cos(\backslash varphi)\; =\; \backslash frac\; =\; \backslash frac\backslash right)\}\; =\; \backslash frac\; \backslash ,\backslash !$ :$\backslash Rightarrow\; \backslash varphi=\backslash cos^\backslash left(\backslash frac\backslash right)\; \backslash ,\backslash !$ For fixed ''P'' the length of the belt depends only on the sum of the radius values ''r''1 + ''r''2, and not on their individual values. 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「Belt problem」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.