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For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

The fixed point with respect to which a pedal curve or pedal triangle is drawn.

Let c=(c_1,...,c_n) be a point in C^n, then the open polydisk is defined by S={z:|z_j-c_j|<|z_j^0-c_j|} for j=1, ..., n.

A point at which three or more polyhedron edges of a polyhedron meet. The concept can also be generalized to a polytope.

A set S with a single point P removed is called a punctured set, written S\{P}.

The catacaustic of the quadrifolium with arbitrary radiant point is a complicated function. A few example are illustrated above.

If a fixed point is added to each group of a special complete series, then the resulting series is complete.

An n-route is defined as a walk of length n with specified initial point in which no line succeeds itself.

A point at which two noncrossing branches of a curve meet with different tangents.

Two curves both containing the point P are tangent at P if they share the same tangent line at P.