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The following table gives the centers of the second Yff circles triangle in terms of the centers of the reference triangle for Kimberling centers X_n with n<=100. X_n center ...

An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., ...

The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...

The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

Dual pairs of linear programs are in "strong duality" if both are possible. The theorem was first conceived by John von Neumann. The first written proof was an Air Force ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

A problem in game theory first discussed by A. Tucker. Suppose each of two prisoners A and B, who are not allowed to communicate with each other, is offered to be set free if ...

Interval arithmetic is the arithmetic of quantities that lie within specified ranges (i.e., intervals) instead of having definite known values. Interval arithmetic can be ...

Let C be a curve and let O be a fixed point. Let P be on C and let Q be the curvature center at P. Let P_1 be the point with P_1O a line segment parallel and of equal length ...