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The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

By way of analogy with the usual tangent tanz=(sinz)/(cosz), (1) the hyperbolic tangent is defined as tanhz = (sinhz)/(coshz) (2) = (e^z-e^(-z))/(e^z+e^(-z)) (3) = ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...

Although Descartes originally used the term "imaginary number" to refer to what is today known as a complex number, in standard usage today, "imaginary number" means a ...

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

An injective module is the dual notion to the projective module. A module M over a unit ring R is called injective iff whenever M is contained as a submodule in a module N, ...