Qvist's theorem

In projective geometry, Qvist's theorem, named after the Finnish mathematician Bertil Qvist [de], is a statement on ovals in finite projective planes.

Standard examples of ovals are non-degenerate (projective) conic sections.

The theorem gives an answer to the question How many tangents to an oval can pass through a point in a finite projective plane?

The answer depends essentially upon the order (number of points on a line −1) of the plane.

Using inhomogeneous coordinates over a field K, |K| = n even, the set the projective closure of the parabola y = x2, is an oval with the point N = (0) as nucleus (see image), i.e., any line y = c, with c ∈ K, is a tangent.