#Differential Geometry - Closed Curves and Rotation Index

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faint bane
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I was looking at this problem from MIT OCW. Could anyone help guide me through with this problem?

image.png
lyric inletBOT
faint bane
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I've noticed a couple things:

  1. I believe we can restrict t to just S = {t | 0 <= t < 1}
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This S is just rotated 2pi/5 for every t+1. This is shown via the Rotation Matrix

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This is a plane curve, and certainly, it is closed. That's given in the problem. It's also periodic... Perhaps a theorem about closed curves could give more insight, as this seems like an extension of Hopf's Theorem on Simple curves