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For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

The continued fraction for ln10 is [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...] (OEIS A016730). The Engel expansion is 2, 3, 7, 9, 104, 510, 1413, ... (OEIS ...

A number of attractive polyhedron compounds consisting of three octahedra. The first (left figues) is the polyhedron dual of the cube 3-compound. These compounds will be ...

A prime triplet is a prime constellation of the form (p, p+2, p+6), (p, p+4, p+6), etc. Hardy and Wright (1979, p. 5) conjecture, and it seems almost certain to be true, that ...

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 ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

A d-repdigit is a number composed of repetition of a single digit (in a given base, generally taken as base 10 unless otherwise specified). For example, the beast number 666 ...

Rule 28 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...