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  "body": "\n## Summary\n\nA torus knot is a [[knot|QYEAZTYGPT]] that lies on the surface of a standard unknotted [[torus|03NM7DZXXC]] in space.\nFor coprime integers $p$ and $q$, the torus knot $T(p, q)$ winds $p$ times around the axis of the torus and $q$ times around its tube.\nTorus knots form one of the three classes in Thurston's division of knots into torus, [[satellite|A1E8TDEVJ9]] and [[hyperbolic|K47G2Q24DT]] knots.\nMany invariants of torus knots can be computed exactly.\n\n## Explanations\n\n### L1 human\n\nPicture a doughnut and wrap a string around its surface without crossing itself.\nGo around the hole $p$ times while going through the hole $q$ times, then close the string up.\nWhen $p$ and $q$ have no common factor you get a single loop, the torus knot $T(p, q)$.\nThe [[trefoil knot|VYTYSVHN4A]] is $T(2, 3)$: twice around the hole and three times through it.\nIf $p$ or $q$ is $\\pm 1$, the loop can be slid off the doughnut and untied.\n",
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  "markdown": "https://math2.tamnd.com/node/NS60VV786W.md",
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  "name": "Torus knot",
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