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The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

A variation of the method of false position for finding roots which fits the function in question with an exponential.

The tetranacci numbers are a generalization of the Fibonacci numbers defined by T_0=0, T_1=1, T_2=1, T_3=2, and the recurrence relation T_n=T_(n-1)+T_(n-2)+T_(n-3)+T_(n-4) ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...