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  "body": "\n## Definition\n\nLet $I \\subseteq \\mathbb{R}$ be an interval, and let $\\gamma \\colon I \\to \\mathbb{R}^n$ be a $C^1$ [[parametrised curve|0JF1XXGWB4]].\nThe curve $\\gamma$ is regular if its [[tangent vector|0D98771SM0]] $\\gamma'(t)$ is not zero for each $t \\in I$.\n\n## Remarks\n\nThe circle $t \\mapsto (\\cos t, \\sin t)$ and each line $t \\mapsto p + t v$ with $v \\ne 0$ are regular.\nThe curve $t \\mapsto (t^2, t^3)$ is not regular, since its tangent vector is zero at $t = 0$.\nThe curve $t \\mapsto (t^3, t^3)$ is not regular at $t = 0$, but its image is a straight line. So regularity is a property of the parametrisation, not of the image.\nA regular curve has an [[arc length parametrisation|00R1JDDV5X]].\n\n## Explanations\n\n### L1 human\n\nA regular curve never stops.\nThe moving point always has non-zero speed, so the curve has no corners or cusps caused by the point coming to rest.\n",
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