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  "body": "\n## Summary\n\nA hyperoval in a finite projective plane of order $n$ is a set of $n + 2$ points with no three on a line.\nIt is the largest possible size of such a set, and it can occur only when $n$ is even.\nWhen $n$ is even, every [[oval|7B03TB64N9]] extends to a hyperoval by adding one point, the nucleus, where all tangents of the oval meet.\nThe classification of hyperovals in $PG(2, 2^h)$ is a long-standing problem of finite geometry.\n\n## Explanations\n\n### L1 human\n\nIn a finite projective plane, how many points can one choose with no three on a line?\nThe answer is at most $n + 2$, and when that many can be chosen, the set is a hyperoval.\nEvery line then meets the set in $0$ or $2$ points, never in exactly one.\nIn the Fano plane, the four points off any line form a hyperoval.\n",
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