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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 ...

Any nonzero rational number x can be represented by x=(p^ar)/s, (1) where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic ...

A homework problem proposed in Steffi's math class in January 2003 asked students to prove that no ratio of two unequal numbers obtained by permuting all the digits 1, 2, ...

A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

The polynomials a_n^((beta))(x) given by the Sheffer sequence with g(t) = (1-t)^(-beta) (1) f(t) = ln(1-t), (2) giving generating function ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle ...

A chamfered tertrahedron, also known as the alternate truncated cube, is a polyhedron obtained by chamfering a regular tetrahedron. The illustration above shows increasing ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...