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If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

The sequence {|_(3/2)^n_|} is given by 1, 1, 2, 3, 5, 7, 11, 17, 25, 38, ... (OEIS A002379). The first few composite |_(3/2)^n_| occur for n=8, 9, 10, 11, 12, 13, 14, 15, 16, ...

A primefree sequence is sequence whose terms are never prime. Graham (1964) proved that there exist relatively prime positive integers a and b such that the recurrence ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

In the most commonly used convention (e.g., Apostol 1967, pp. 205-207), the second fundamental theorem of calculus, also termed "the fundamental theorem, part II" (e.g., ...