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A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

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The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

A single-valued function is function that, for each point in the domain, has a unique value in the range. It is therefore one-to-one or many-to-one. A single-valued complex ...

The hyperbolic functions sinhz, coshz, tanhz, cschz, sechz, cothz (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and ...