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  "body": "\n## Summary\n\nAn oval in a projective plane is a set of points that behaves like a conic.\nNo line meets it in more than two points, and at each of its points there is exactly one tangent line.\nIn a finite plane of order $n$, an oval is the same as a set of $n + 1$ points with no three on a line.\nNon-degenerate [[projective conics|R3TMVHTP3A]] are ovals.\n[[Segre's theorem|SPFP3GHVYJ]] says that in $PG(2, q)$ with $q$ odd there are no others.\nFor $q$ even, ovals extend to [[hyperovals|RNG2A8BFVZ]], and for $q \\ge 8$ there are ovals that are not conics.\n\n## Explanations\n\n### L1 human\n\nA circle meets any line in at most two points, and at each of its points it has a single tangent.\nAn oval keeps these two properties, stated only in terms of points and lines, so it makes sense in any projective plane.\nIn the Fano plane, the four points off a fixed line form a set with no three on a line; any three of them form an oval.\nOvals are the starting point for the study of arcs and caps in finite geometry.\n",
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