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A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

By analogy with the lemniscate functions, hyperbolic lemniscate functions can also be defined arcsinhlemnx = int_0^x(1+t^4)^(1/2)dt (1) = x_2F_1(-1/2,1/4;5/4;-x^4) (2) ...

An Archimedean spiral with polar equation r=a/theta. (1) The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in ...

Given a sequence of real numbers a_n, the infimum limit (also called the limit inferior or lower limit), written lim inf and pronounced 'lim-inf,' is the limit of ...

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

The inverse haversine function hav^(-1)(z) is defined by hav^(-1)(z)=2sin^(-1)(sqrt(z)). (1) The inverse haversine is implemented in the Wolfram Language as ...

A system of coordinates obtained by inversion of the oblate spheroids and one-sheeted hyperboloids in oblate spheroidal coordinates. The inverse oblate spheroidal coordinates ...

A system of coordinates obtained by inversion of the prolate spheroids and two-sheeted hyperboloids in prolate spheroidal coordinates. The inverse prolate spheroidal ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

A right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an ...