(k, d)-arcs in A Projective Plane
A (k, d)-arc (k, d > 1) in a finite projective plane π (not necessarily Desarguesian) is a set, A 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. A (k, 2)-arc is a k-arc and may be referred to as simply an arc if the size is not a concern.
The number of points k of a (k, d)-arc A in a projective plane of order q is at most qd + d − q. When equality occurs, one calls A a maximal arc.
Hyperovals are maximal arcs. Complete arcs need not be maximal arcs.
Read more about this topic: Arc (projective Geometry)
Famous quotes containing the word plane:
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)