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To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...

The tribonacci numbers are a generalization of the Fibonacci numbers defined by T_1=1, T_2=1, T_3=2, and the recurrence equation T_n=T_(n-1)+T_(n-2)+T_(n-3) (1) for n>=4 ...

A (0,1)-matrix is an integer matrix in which each element is a 0 or 1. It is also called a logical matrix, binary matrix, relation matrix, or Boolean matrix. The number of ...

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...

An amphichiral knot is a knot that is capable of being continuously deformed into its own mirror image. More formally, a knot K is amphichiral (also called achiral or ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...