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The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...

A connection game is a board game in which players compete to develop or complete a type of topological connection with their pieces. This could involve forming a path ...

The discrete Fourier transform of length N (where N is even) can be rewritten as the sum of two discrete Fourier transforms, each of length N/2. One is formed from the ...

The dodecahedron-small triambic icosahedron compound is a stellated form of a truncated icosahedron, but a different truncation than in the truncated icosahedron Archimedean ...

The term "lobster" is used to refer either to a particular polyiamond or to a class of tree called a lobster graph. When referring to polyiamonds, the lobster is the ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Two totally ordered sets (A,<=) and (B,<=) are order isomorphic iff there is a bijection f from A to B such that for all a_1,a_2 in A, a_1<=a_2 iff f(a_1)<=f(a_2) (Ciesielski ...

A polyform of 30-60-90 triangles. The name was coined by Ed Pegg, Jr. because of the 30-60-90 triangle's use in mechanical drawing and drafting. The Eternity puzzle is based ...