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A triangle center (sometimes simply called a center) is a point whose trilinear coordinates are defined in terms of the side lengths and angles of a triangle and for which a ...

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

A tiling consisting of a rhombus such that 17 rhombuses fit around a point and a second tile in the shape of six rhombuses stuck together. These two tiles can fill the plane ...

A topological space M satisfying some separability (i.e., it is a T2-space) and countability (i.e., it is a paracompact space) conditions such that every point p in M has a ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular ...

There are nine possible types of isolated singularities on a cubic surface, eight of them rational double points. Each type of isolated singularity has an associated normal ...

The set of points of X fixed by a group action are called the group's set of fixed points, defined by {x:gx=x for all g in G}. In some cases, there may not be a group action, ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...