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

The point at which the three lines connecting the polygon vertices of perspective triangles (from a point) concur, sometimes also called the homology center, pole, or, in ...

Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...

For a unit circle with parametric equations x = cost (1) y = sint, (2) the negative pedal curve with respect to the pedal point (r,0) is x_n = (r-cost)/(rcost-1) (3) y_n = ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

The lines joining the vertices A, B, and C of a given triangle DeltaABC with the circumcenters of the triangles DeltaBCO, DeltaCAO, and DeltaABO (where O is the circumcenter ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...