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Given four points, A, B, C, and H, let H be the orthocenter of DeltaABC. Then A is the orthocenter DeltaHBC, B is the orthocenter of DeltaHAC, and C is the orthocenter of ...

A flexible polyhedron due to C. Schwabe (with the appearance of having four horns) which flexes from one totally flat configuration to another, passing through intermediate ...

An asymptotic direction at a point p of a regular surface M in R^3 is a direction in which the normal curvature of M vanishes. 1. There are no asymptotic directions at an ...

A point of discontinuity, also called a leap.

The point that inversion of a curve is performed with respect to.

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

Let P=alpha:beta:gamma be a point not on a sideline of a reference triangle DeltaABC. Let A^' be the point of intersection AP intersection BC, B^'=BP intersection AC, and ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.