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  "body": "\n## Example\n\nThe *unknot* is the round circle\n$$U = \\set{(x, y, 0) \\in \\R^3 : x^2 + y^2 = 1},$$\nthe image of the map $t \\mapsto (\\cos t, \\sin t, 0)$, which is continuous and injective on the [[circle|060W5CBZP6]] $\\R / 2\\pi\\Z$.\nSo $U$ is a [[knot|QYEAZTYGPT]], and it is tame since it is equivalent to a square, a closed polygon.\nAny knot equivalent to $U$ is also called an unknot, or a trivial knot.\n\n## Remarks\n\nThe unknot bounds the flat unit disk, a [[Seifert surface|K866ND3WF7]] of genus $0$, and a knot is trivial exactly when it bounds an embedded disk.\nIts [[knot group|AQVHM3FP0D]] is $\\Z$, its [[crossing number|SWJZ4QRF9W]] is $0$, and its Alexander and Jones polynomials are $1$.\nA tame knot with knot group $\\Z$ is the unknot.\nRecognizing the unknot from a diagram is the [[unknotting problem|VXSD46NRX0]]; Wolfgang Haken showed that it is decidable.\nSome diagrams of the unknot are complicated, and untangling them may first require more crossings.\n\n## Explanations\n\n### L1 human\n\nThe unknot is a plain loop of string with no knot in it, like a rubber band.\nAny loop that can be moved in space, without cutting, to a round circle is also an unknot.\nIt is the starting point of knot theory: to show that a knot is really knotted is to show that it is not the unknot.\n",
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