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A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

The involute of a parabola x = at^2 (1) y = at (2) is given by x_i = -(atsinh^(-1)(2t))/(2sqrt(4t^2+1)) (3) y_i = a(1/2t-(sinh^(-1)(2t))/(4sqrt(4t^2+1))). (4) Defining ...

A pentahedron is polyhedron having five faces. Because there are two pentahedral graphs, there are two convex pentahedra, corresponding to the topologies of the square ...

Given algebraic numbers a_1, ..., a_n it is always possible to find a single algebraic number b such that each of a_1, ..., a_n can be expressed as a polynomial in b with ...

There are a number of functions in mathematics denoted with upper or lower case Qs. 1. The nome q. 2. A prefix denoting q-analogs and q-series. 3. Q_n or q_n with n=0, 1, 2, ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

A Shanks (a,b)-chain is a sequence of primes p_i of the form p_(i+1)=ap_i^2-b, with a and b integers. On Sep. 1, 2000, P. Leyland found a (4, 17)-chain of length 6, and on ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

The base-20 notational system for representing real numbers. The digits used to represent numbers using vigesimal notation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, ...

An ordered factorization is a factorization (not necessarily into prime factors) in which a×b is considered distinct from b×a. The following table lists the ordered ...