Lot’s more! 

Since it does not look like I will be learning to write my own applets any time soon (or getting any papers graded!) I have continued using the Interactive Physics work-around to generate a gallery of these polar graphs.  If you are learning (or teaching) graphing in polar coordinates, I  hope you find these helpful.

NOTE: I am not claiming that these are the fastest ways to get these graphs.  There are many graphing programs that can sketch these diagrams more quickly.  But I think these might help you to build an intuitive understanding of why the graphs come out the way they do.

Reminder: I am using Anton’s idea about an ant that walks along a rotating clock arm.  The ant’s position along the clock arm is give by the polar function r=f(θ).  These animations show how the polar curve is constructed as the ant’s position changes while the clock arm rotates.

Anyway, here they are.  Click on a video to play it.  And it’s easier to see what’s happening if you expand the video to full-screen mode.

A CIRCLE on the x-axis

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A CIRCLE on the y-axis

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 A CARDIOID — symmetrical w/ y-axis

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ANOTHER CARDIOID — symmetrical w/ x-axis

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A CARDIOID with an inner loop

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A ROSE PETAL with 3 loops

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ANOTHER ROSE PETAL with 3 loops — what’s different about it?

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 A ROSE PETAL WITH 5 LOOPS

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OK, that’s all for now.  If you had another one of these that you were eager to see, post a comment and I’ll try to add the one you want to the gallery.