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A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

With n cuts of a torus of genus 1, the maximum number of pieces which can be obtained is N(n)=1/6(n^3+3n^2+8n). The first few terms are 2, 6, 13, 24, 40, 62, 91, 128, 174, ...

The total graph T(G) of a graph G has a vertex for each edge and vertex of G and an edge in T(G) for every edge-edge, vertex-edge, and vertex-vertex adjacency in G ...

The functions (also called the circular functions) comprising trigonometry: the cosecant cscx, cosine cosx, cotangent cotx, secant secx, sine sinx, and tangent tanx. However, ...

Truncation is the removal of portions of solids falling outside a set of symmetrically placed planes. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

A finite simple group of Lie-type. The following table summarizes the types of twisted Chevalley groups and their respective orders. In the table, q denotes a prime power and ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

Let X_1, ..., X_N be a sequence of independent observations of a random variable X, and let the number of observations N itself be chosen at random. Then Wald's equation ...

(Bailey 1935, p. 25), where _7F_6(a_1,...,a_7;b_1,...,b_6) and _4F_3(a_1,...,a_4;b_1,b_2,b_3) are generalized hypergeometric functions with argument z=1 and Gamma(z) is the ...

The surface area of a spherical segment. Call the radius of the sphere R, the upper and lower radii b and a, respectively, and the height of the spherical segment h. The zone ...