Arc (projective geometry)

Arc (Projective Geometry)

Arc (projective geometry)

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Description:
In mathematics, a (k,&nbsp;d)-arc (k,&nbsp;d&nbsp;&ge;&nbsp;1) of order q in a finite projective plane &pi; (not necessarily Desarguesian) is a set of k points of <math>pi</math> 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.

Special cases

The number of points k of A is at most qd&nbsp;+&nbsp;d&nbsp;&minus;&nbsp;q. When equality occurs, one speak of a maximal arc.

(q&nbsp;+&nbsp;1,&nbsp;2)-arcs are precisely the ovals and (q&nbsp;+&nbsp;2,&nbsp;2)-arcs are precisely the hyperovals (which can only occur for even q).

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