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”Šw‚É‚¨‚¢‚Ĥ±Æ­×½i—…: annulus, ×Ã݌ê‚Å¢¬‚³‚¢ŠÂ£‚ðˆÓ–¡‚·‚éj‚ ‚é‚¢‚͉~ŠÂ‚Ƃͤ—Ö‚ÌŒ`‚ð‚µ‚½‘Ώۤ“Á‚É 2 ‚‚̓¯S‰~‚É‚æ‚Á‚Ĉ͂܂ꂽ—̈æ‚Å‚ ‚é¡

ŠJ±Æ­×½‚͉~’Œ‘¤–ʁi‰~“›j S1 × (0,1) ‚⌊‚ ‚«•½–Ê R2 {(0, 0)} ‚É“¯‘Š‚Å‚ ‚é¡

±Æ­×½‚̖ʐς͔¼Œa R ‚Ì‘å‚«‚¢‰~‚̖ʐς©‚甼Œa r ‚̏¬‚³‚¢‰~‚̖ʐςðˆø‚¢‚½‚à‚Ì‚Å‚ ‚éF

A = π R 2 π r 2 = π ( R 2 r 2 ) . {\displaystyle A=\pi R^{2}-\pi r^{2}=\pi (R^{2}-r^{2}).} ±Æ­×½‚̖ʐςͱƭ׽‚Ì’†‚ÉŠ®‘S‚É’u‚¯‚éÅ’·‚̐ü•ª‚Ì’·‚³i“Y•t}‚Ì 2dj‚©‚瓾‚ç‚ê‚é¡‚±‚ê‚ÍËßÀºÞ×½‚̒藝‚É‚æ‚Á‚ďؖ¾‚Å‚«‚顱ƭ׽‚Ì’†‚ÉŠ®‘S‚É’u‚¯‚éÅ’·‚̐ü•ª‚͏¬‚³‚¢‰~‚ɐڂµ¤‚»‚Ì“_‚É‚¨‚¯‚锼Œa‚Æ’¼Šp‚ð‚È‚·¡‚µ‚½‚ª‚Á‚Ä d ‚Æ r ‚ÍŽÎ•Ó R ‚Ì’¼ŠpŽOŠpŒ`‚ÌŽc‚è‚Ì•Ó‚Ì’·‚³‚Å‚ ‚褖ʐς͎Ÿ‚Å—^‚¦‚ç‚ê‚éF

A = π ( R 2 r 2 ) = π d 2 . {\displaystyle A=\pi (R^{2}-r^{2})=\pi d^{2}.} –ʐς͔÷•ªÏ•ªŠw‚É‚æ‚Á‚Ä‚àŒvŽZ‚Å‚«‚顱ƭ׽‚𕝠¤–ÊÏ 2πρ ‚Ì–³ŒÀŒÂ‚Ì–³ŒÀ¬±Æ­×½‚É•ªŠ„‚µ¤ρ = r ‚©‚ç ρ = R ‚܂Őϕª‚·‚éF

A = r R 2 π ρ d ρ = π ( R 2 r 2 ) . {\displaystyle A=\int _{r}^{R}2\pi \rho \,d\rho =\pi (R^{2}-r^{2}).} θ ׼ޱ݂ɑ΂·‚é "îŒ`"i‰~ŠÂîŒ`j‚̖ʐςÍ

A = θ 2 ( R 2 r 2 ) . {\displaystyle A={\frac {\theta }{2}}(R^{2}-r^{2}).}

•¡‘f\‘¢[•ÒW]

•¡‘f‰ðÍ‚É‚¨‚¢‚Ĥ•¡‘f”•½–ʂ̱ƭ׽ ann(a; r, R) ‚Í

r < | z a | < R {\displaystyle r<|z-a|<R} ‚Å’è‹`‚³‚ê‚éŠJ—̈æ‚Ì‚±‚Æ‚ðŒ¾‚¤¡r ‚ª 0 ‚Ì‚Æ‚«¤‚±‚̗̈æ‚Í“_ a ‚𒆐S‚Æ‚·‚锼Œa R ‚ÌŒŠ‹ó‚«‰~” (punctured disk) ‚Å‚ ‚é¡

•¡‘f•½–Ê‚Ì•”•ªW‡‚Æ‚µ‚Ĥ±Æ­×½‚ÍØ°Ïݖʂƍl‚¦‚邱‚Æ‚ª‚Å‚«‚顱ƭ׽‚Ì•¡‘f\‘¢‚Í”ä r/R ‚݂̂Ɉˑ¶‚·‚é¡ŽÀÛ¤Še±Æ­×½ ann(a; r, R) ‚Í z ? za/R ‚Æ’u‚­‚±‚Æ‚É‚æ‚褑傫‚¢•û‚Ì”¼Œa‚ª 1 ‚ÅŒ´“_‚É’†S‚ðŽ‚Â•W€±Æ­×½ ann(0; r/R, 1) ‚ɐ³‘¥‚ÉŽÊ‚é¡

±ÀÞϰق̎O‰~’藝‚͐³‘¥ŠÖ”‚ª±Æ­×½‚Ì“à•”‚ÅŽæ‚蓾‚éÅ‘å’l‚ɂ‚¢‚ďq‚ׂé¡

ŠÖ˜A€–Ú[•ÒW]

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ŠO•”Øݸ[•ÒW]

Weisstein, Eric W. "Annulus". MathWorldi‰pŒêj. 
annulus - PlanetMath.i‰pŒêj
Hazewinkel, Michiel, ed. (2001), "Two-dimensional annulus", Encyclopaedia of Mathematics, Springer, ISBN 978-1-55608-010-4 
Annulus definition and properties With interactive animation
Area of an annulus, formula With interactive animation
o“T:Wikipedia
2018/12/15 20:31
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