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Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

Consider a network of n resistors R_i so that R_2 may be connected in series or parallel with R_1, R_3 may be connected in series or parallel with the network consisting of ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

The star polygon {8/3}.

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...

In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...