Curve stitching on a unit circle

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Freely slide the two bars, can you describe the relation between n and k such that
1. The curve stitching graph passing through all the points on the circle.
2. For the other cases, some points on the circle are missing on the curve stitching graph, would you find some conditions that the point are missing?
3. Can you describe when the curve stitching graph is a simple polygon?


Created with GeoGebraShared by kkpoon
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