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Let A be an edge cut of a connected graph G. Then the cyclic edge connectivity lambda_c(G) is the size of a smallest cyclic edge cut, i.e., a smallest edge cut A such that ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

An n×n complex matrix A is called positive definite if R[x^*Ax]>0 (1) for all nonzero complex vectors x in C^n, where x^* denotes the conjugate transpose of the vector x. In ...

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...