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The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...

Specifying two adjacent angles A and B and the side between them c uniquely (up to geometric congruence) determines a triangle with area K=(c^2)/(2(cotA+cotB)). (1) The angle ...

A convex body in Euclidean space that is centrally symmetric with center at the origin is determined among all such bodies by its brightness function (the volume of each ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

A highly structured geometric object used to study groups which act upon them.

The parametric equations for a catenary are x = t (1) y = acosh(t/a), (2) giving the evolute as x = t-a/2sinh((2t)/a) (3) y = 2acosh(t/(2a)). (4) For t>0, the evolute has arc ...

A geometric figure which touches only the vertices (or other extremities) of another figure.

An n-dimensional closed disk of radius r is the collection of points of distance <=r from a fixed point in n-dimensional Euclidean space. Krantz (1999, p. 3) uses the symbol ...

A set X is called a "cone" with vertex at the origin if for any x in X and any scalar a>=0, ax in X.