翻訳と辞書 Words near each other ・ Hypocrita speciosa ・ Hypocrita strigifera ・ Hypocrita temperata ・ Hypocrita toulgoetae ・ Hypocrita turbida ・ Hypocrita variabilis ・ Hypocrita wingerteri ・ Hypocrite Channel ・ Hypocrite in a Hippy Crypt ・ Hypocrite in a Pouffy White Dress ・ Hypocrites (film) ・ Hypocritical Oaf ・ Hypocryptothrix ・ Hypoctonus ・ Hypoctonus formosus ・ Hypocycloid ・ Hypocysta ・ Hypocysta adiante ・ Hypocysta angustata ・ Hypocysta aroa ・ Hypocysta euphemia ・ Hypocysta irius ・ Hypocysta metirius ・ Hypocysta pseudirius ・ Hypocystina ・ Hypodactylia ・ Hypodactylus ・ Hypodactylus adercus ・ Hypodactylus araiodactylus ・ Hypodactylus fallaciosus 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 Hypocycloid ： ウィキペディア英語版 Hypocycloid In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle. ==Properties== If the smaller circle has radius ''r'', and the larger circle has radius ''R'' = ''kr'', then the parametric equations for the curve can be given by either: :$x\; (\backslash theta)\; =\; (R\; -\; r)\; \backslash cos\; \backslash theta\; +\; r\; \backslash cos\; \backslash left(\; \backslash frac\; \backslash theta\; \backslash right)$ :$y\; (\backslash theta)\; =\; (R\; -\; r)\; \backslash sin\; \backslash theta\; -\; r\; \backslash sin\; \backslash left(\; \backslash frac\; \backslash theta\; \backslash right),$ or: :$x\; (\backslash theta)\; =\; r\; (k\; -\; 1)\; \backslash cos\; \backslash theta\; +\; r\; \backslash cos\; \backslash left(\; (k\; -\; 1)\; \backslash theta\; \backslash right)\; \backslash ,$ :$y\; (\backslash theta)\; =\; r\; (k\; -\; 1)\; \backslash sin\; \backslash theta\; -\; r\; \backslash sin\; \backslash left(\; (k\; -\; 1)\; \backslash theta\; \backslash right).\; \backslash ,$ If ''k'' is an integer, then the curve is closed, and has ''k'' cusps (i.e., sharp corners, where the curve is not differentiable). Specially for k=2 the curve is a straight line and the circles are called Cardano circles. Girolamo Cardano was the first to describe these hypocycloids and their applications to high-speed printing. If ''k'' is a rational number, say ''k'' = ''p''/''q'' expressed in simplest terms, then the curve has ''p'' cusps. If ''k'' is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius ''R'' − 2''r''. Each hypocycloid (for any value of ''r'') is a brachistochrone for the gravitational potential inside a homogeneous sphere of radius ''R''. 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「Hypocycloid」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.