File:PolarArclength.png

Revision as of 23:39, 26 July 2019 by Mag1c (talk | contribs) ([asy] import graph; size(120); real f(real t) {return 1;} path g=polargraph(f,pi/4,pi/3,10000, operator --); draw(g,black); draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2))); label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S); label("$f(\theta)$...)
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PolarArclength.png(404 × 290 pixels, file size: 13 KB, MIME type: image/png)

Summary

[asy] import graph; size(120); real f(real t) {return 1;} path g=polargraph(f,pi/4,pi/3,10000, operator --); draw(g,black); draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2))); label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S); label("$f(\theta)$",(1/sqrt(2)/2,1/sqrt(2)/2),E); draw((1/2,sqrt(3)/2)--(1/sqrt(2),1/sqrt(2))--(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5,sqrt(3)/2-(1/2-1/sqrt(2))*0.5)--cycle,red); draw(rightanglemark((1/sqrt(2),1/sqrt(2)), (1/2,sqrt(3)/2),(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5,sqrt(3)/2-(1/2-1/sqrt(2))*0.5),1.6)); label("$df$", ((1/2+1/2-(1/sqrt(2)-sqrt(3)/2)*0.5)/2 ,(sqrt(3)/2+sqrt(3)/2-(1/2-1/sqrt(2))*0.5)/2 ),W); label("$ds$", ((1/sqrt(2)+1/2-(1/sqrt(2)-sqrt(3)/2)*0.5)/2 ,(1/sqrt(2)+sqrt(3)/2-(1/2-1/sqrt(2))*0.5)/2 ), NE); draw("$f(\theta+d\theta)$",(0+ (1/2-1/sqrt(2))*.8,0+ (sqrt(3)/2-1/sqrt(2))*.8 )--(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5 + (1/2-1/sqrt(2))*.8,sqrt(3)/2-(1/2-1/sqrt(2))*0.5 + (sqrt(3)/2-1/sqrt(2))*.8),NW,Bars,PenMargins); draw((1,0)--(0,0)--(0,1)); [/asy]

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current23:39, 26 July 2019Thumbnail for version as of 23:39, 26 July 2019404 × 290 (13 KB)Mag1c (talk | contribs)[asy] import graph; size(120); real f(real t) {return 1;} path g=polargraph(f,pi/4,pi/3,10000, operator --); draw(g,black); draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2))); label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S); label("$f(\theta)$...
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