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  "body": "\n## Definition\n\nLet $a \u003c b$, and let $\\gamma \\colon [a, b] \\to \\mathbb{R}^n$ be a [[parametrised curve|0JF1XXGWB4]].\nThe curve $\\gamma$ is closed if $\\gamma(a) = \\gamma(b)$.\nA closed curve is simple if, in addition, $\\gamma(s) \\ne \\gamma(t)$ for all $s \u003c t$ in $[a, b]$ other than the pair $s = a$, $t = b$.\n\n## Remarks\n\nThe unit circle $\\gamma(t) = (\\cos t, \\sin t)$, $t \\in [0, 2\\pi]$, is a simple closed curve.\nThe curve $t \\mapsto (\\sin 2t, \\sin t)$, $t \\in [0, 2\\pi]$, is closed but not simple: it passes through the origin at $t = 0$, $t = \\pi$ and $t = 2\\pi$.\nThe line integral of a vector field around a closed curve is often written $\\oint_\\gamma F \\cdot d\\mathbf{r}$. It is the circulation of $F$ around $\\gamma$.\nA simple closed curve in the plane bounds a region. This is the setting of [[Green's theorem|0HR3N02317]].\n\n## Explanations\n\n### L1 human\n\nA closed curve is a path that comes back to where it started, like a lap around a track.\nIt is simple if it never crosses itself on the way.\n",
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