Arc (projective geometry)
- Arc (projective geometry)
Let be a finite projective plane (not necessarily Desarguesian) of order "q". A -arc "A" () is a set of "k" points of 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.
pecial cases
The number of points "k" of "A" is at most . When equality occurs, one speak of a maximal arc.
-arcs are precisely the ovals and -arcs are precisely the hyperovals (which can only occur for even "q").
External links
*springer|id=A/a120250|title=Arc|author=C.M. O'Keefe
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