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The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

A connex is a geometric form introduced by Clebsch (1872) that included as special cases the curve considered as a point locus and the curve considered as a line envelope ...

Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...

The normal vector, often simply called the "normal," to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed ...

The Lyapunov characteristic exponent [LCE] gives the rate of exponential divergence from perturbed initial conditions. To examine the behavior of an orbit around a point ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

The vertex connectivity kappa(G) of a graph G, also called "point connectivity" or simply "connectivity," is the minimum size of a vertex cut, i.e., a vertex subset S subset= ...

The BCI triangle DeltaA^'B^'C^' of a triangle DeltaABC with incenter I is defined by letting A^' be the center of the incircle of DeltaBCI, and similarly defining B^' and ...