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Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

cos(pi/(15)) = 1/8(sqrt(30+6sqrt(5))+sqrt(5)-1) (1) cos((2pi)/(15)) = 1/8(sqrt(30-6sqrt(5))+sqrt(5)+1) (2) cos((4pi)/(15)) = 1/8(sqrt(30+6sqrt(5))-sqrt(5)+1) (3) ...

Define the correlation integral as C(epsilon)=lim_(N->infty)1/(N^2)sum_(i,j=1; i!=j)^inftyH(epsilon-|x_i-x_j|), (1) where H is the Heaviside step function. When the below ...

A general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 for y!=0 a function on the tangent bundle T(M), and homogeneous of degree 1 in y. ...

A special case of nim played by the following rules. Given a heap of size n, two players alternately select a heap and divide it into two unequal heaps. A player loses when ...

The inversive distance is the natural logarithm of the ratio of two concentric circles into which the given circles can be inverted. Let c be the distance between the centers ...

The distribution with probability density function and distribution function P(r) = (re^(-r^2/(2s^2)))/(s^2) (1) D(r) = 1-e^(-r^2/(2s^2)) (2) for r in [0,infty) and parameter ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

The Napoleon-Feuerbach cubic is the pivotal isogonal cubic with nine-point center N as the pivot point. It therefore has trilinear equation ...