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There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

The terms of equational logic are built up from variables and constants using function symbols (or operations). Identities (equalities) of the form s=t, (1) where s and t are ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

Suppose a line L^' meets sidelines BC, CA, and AB in points A^', B^', and C^', respectively. Let A^('') be the reflection of A^' about the midpoint of segment BC, and ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...