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A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

A Thâbit ibn Kurrah number, sometimes called a 321-number, is a number of the form K_n=3·2^n-1. The first few for n=0, 1, ... are 2, 5, 11, 23, 47, 95, 191, 383, 767, ... ...

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma ...

The triangle graph is the cycle graph C_3, which is isomorphic to the complete graph K_3 as well as to the complete tripartite graph K_(3×1)=K_(1,1,1) and the triangular ...

The cubic curve defined by ax^3+bx^2+cx+d=xy with a!=0. The curve cuts the axis in either one or three points. It was the 66th curve in Newton's classification of cubics. ...

The polyhedron compound of the truncated cube and its dual, the small triakis octahedron. The compound can be constructed from a truncated cube of unit edge length by ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), .... Then Weddle's rule approximating the integral of ...