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A group is called a free group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

A figurate number of the form g_n=2n-1 giving the area of the square gnomon obtained by removing a square of side n-1 from a square of side n, g_n = n^2-(n-1)^2 (1) = 2n-1. ...

The skewness of a graph G is the minimum number of edges whose removal results in a planar graph (Harary 1994, p. 124). The skewness is sometimes denoted mu(G) (Cimikowski ...

The gyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating one of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn. It is ...

A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...

The Herschel nonahedron is a canonical polyhedron whose skeleton is the Herschel graph. It has 11 vertices, 18 edges, and 9 faces. Of the edges, 6 are short and 12 are long. ...

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

In conical coordinates, Laplace's equation can be written ...