Trapping a sphere in a trefoil knot

Question

Is it possible to trap a sphere in the center of a trefoil knot? It seems like with three points of contact it should be possible. Admittedly not big into math, but a craftsman who loves trapping marbles. Sincerely appreciate any thoughts or suggestions.

Answer 1

This depends on where you want to trap the sphere. Usually, a trefoil goes around the outside (major radius) of the torus twice and smaller (minor) three times. We sometimes call this a (3,2) torus knot. The best place to put a marble or sphere would be the center of the torus, but this only will have three points of contact, and as TonyK stated, we need 4 if we want to hold the sphere.

But, if we use the trefoil where we switch the meridian and longitude, we get three "strands" which flow around the torus, a (2,3) torus knot. See some useful pictures here. Then a few marbles could roll around inside the area where the torus would be, and I believe, be trapped.

If you want to let the trefoil be in some other configuration where it doesn't necessarily lie in a torus, I am sure you can get it to hold a sphere stationary. Hope this helped.

Answer 2

Here is an example suggested by Scott Carnahan in response to a different question, "Hanging a ball with string," which I include in case it might yield some intuition.

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