Arc (projective geometry)
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Let π be a finite projective plane (not necessarily Desarguesian) of order q. A (k,d)-arc A (
) is a set of k points of π such that each line intersects A in at most d points, and there is at least one line that does intersect A in d points.
[edit] Special cases
The number of points k of A is at most qd + d − q. When equality occurs, one speak of a maximal arc.
(q + 1,2)-arcs are precisely the ovals and (q + 2,2)-arcs are precisely the hyperovals (which can only occur for even q).
[edit] External links
- C.M. O'Keefe (2001), “Arc”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
