So in the process of giving us a crude definition of a trefoil knot, our professor talks a bit about a function on a torus.(adsbygoogle = window.adsbygoogle || []).push({});

If we view the torus as the identification of sides of a square, and define a function y=(p/q)x, then we may only go from the bottom left corner (0,0) to the top right corner (1,1) (I guess forming a knot) if (p,q)=1. Two questions...

1) Isn't any function y=(m/n)x the same as a function y=(p/q)x with (p,q)=1?

2) Is there a simple way to understand why the (p,q) must be 1, or is it something not so trivial?

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# P,q Trefoil Knot

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