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A triangle line lalpha+mbeta+ngamma=0 defined relative to a reference triangle is called a central line iff l:m:n is a triangle center (Kimberling 1998, p. 127). If l:m:n is ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

Calculus I

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). ...

Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...

An International Standard Book Number (ISBN) is a code used to uniquely identify a book together. It also uniquely encodes the book's publisher and includes information about ...

The set of points, known as boundary points, which are members of the set closure of a given set S and the set closure of its complement set. The boundary is sometimes called ...

The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the ...