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  "body": "\n## Summary\n\nA differentiable curve is a [[parametrised curve|0G7WM8DX4P]] whose coordinate functions have continuous derivatives up to some order $k \\ge 1$.\nIt is the basic object of the differential geometry of curves.\nTangent vectors, arc length, curvature and torsion are all defined for differentiable curves of suitable order.\n\n## Explanations\n\n### L1 human\n\nThink of a point that moves smoothly through space, with a velocity at each moment.\nA differentiable curve records the position of that point as a function of time.\nBeing differentiable means that the velocity exists and changes continuously.\nFor example, $t \\mapsto (\\cos t, \\sin t, t)$ is a differentiable curve, the helix, which winds around a cylinder.\n",
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