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  "body": "\n## Summary\n\nThe evolute of a plane curve is the curve traced by its centres of curvature.\nEquivalently, it is the envelope of the normal lines of the curve.\nThe evolute stops moving, and typically has a cusp, at the vertices of the curve, the points where the derivative of the curvature vanishes.\n\n## Explanations\n\n### L1 human\n\nAt each point of a curve, draw the [[osculating circle|NWSFMCRWHJ]], the circle that hugs the curve best.\nAs the point moves, the centre of that circle moves too, and its path is the evolute.\nFor a circle, the centre never moves, so the evolute is a single point.\nFor the parabola $y = x^2$, the evolute is a curve with a sharp cusp, called a semicubical parabola.\n",
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