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For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

The Euclidean metric is the function d:R^n×R^n->R that assigns to any two vectors in Euclidean n-space x=(x_1,...,x_n) and y=(y_1,...,y_n) the number ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient. In graph theory, excess refers to the quantity e=n-n_l(v,g) (1) for a v-regular ...

The w-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. Setting f_n(1)=f_n (1) give a Fermat-Lucas number. The first few Fermat-Lucas ...

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if 1. L(x,y) is differentiable at ...

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a "reflected" code, or more ...

The McGee graph is a cubic symmetric graph on 24 nodes and 36 edges which is the unique 7-cage graph. It can be constructed as the union of the two leftmost subgraphs ...

Given a complete graph K_n which is two-colored, the number of forced monochromatic triangles is at least {1/3u(u-1)(u-2) for n=2u; 2/3u(u-1)(4u+1) for n=4u+1; ...