Three geodesics on a cone

These dynamic diagrams represent how a necklace with a pendant will hang on a cone. The necklace follows a geodesic on the surface of the cone. The left diagram shows the "unfolded" cone and the right diagram shows the actual cone. The straight lines in the left diagram become the curves shown in the right diagram once the paper has been rolled into a cone. The orange line represents a necklace wrapped once around the cone. The purple and red lines represent two and three wraps. See Numberplay for the puzzle this is based on.

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