File:PolarArclength.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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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:39, 27 July 2019 | | 404 × 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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