Arc (Projective Geometry)

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In mathematics, a (*k*, *d*)-**arc** (*k*, *d* ≥ 1) of order *q* in a finite projective plane *π* (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* + *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*).

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