Oval

Summary

An oval in a projective plane is a set of points that behaves like a conic. No line meets it in more than two points, and at each of its points there is exactly one tangent line. In a finite plane of order $n$, an oval is the same as a set of $n + 1$ points with no three on a line. Non-degenerate projective conics are ovals. Segre's theorem says that in $PG(2, q)$ with $q$ odd there are no others. For $q$ even, ovals extend to hyperovals, and for $q \ge 8$ there are ovals that are not conics.