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  "body": "\n## Summary\n\nA $k$-arc in a finite [[projective plane|DANFNN8C4Y]] is a set of $k$ points with no three on a common line.\nIn a plane of order $n$ a $k$-arc has at most $n + 2$ points, and at most $n + 1$ points when $n$ is odd.\nArcs of maximal size, such as conics, are central objects of finite geometry and are linked to maximum distance separable codes.\n\n## Explanations\n\n### L1 human\n\nPick points in a finite plane so that no line passes through three of them.\nSuch a set is an arc, a discrete version of a curve that bends everywhere.\nIn the plane over the field with $q$ elements, the points $(1 : t : t^2)$ for $t$ in the field, together with $(0 : 0 : 1)$, form an arc with $q + 1$ points.\nIt is the finite analogue of a parabola together with its point at infinity.\n",
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