(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:
“It was the most ungrateful and unjust act ever perpetrated by a republic upon a class of citizens who had worked and sacrificed and suffered as did the women of this nation in the struggle of the Civil War only to be rewarded at its close by such unspeakable degradation as to be reduced to the plane of subjects to enfranchised slaves.”
—Anna Howard Shaw (1847–1919)