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common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse...

functions are: hyperbolic sine "sinh" (/ˈsɪŋ, ˈsɪntʃ, ˈʃaɪn/), hyperbolic cosine "cosh" (/ˈkɒʃ, ˈkoʊʃ/), from which are derived: hyperbolic tangent "tanh" (/ˈtæŋ...

c\,}}.\,} The cosine of angle A is the hyperbolic tangent of the adjacent leg divided by the hyperbolic tangent of the hypotenuse. cos ⁡ A = tanh(adjacent)...

paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...

spherical geometry and hyperbolic geometry. In higher dimensions, an analogous quadratic equation applies to systems of pairwise tangent spheres or hyperspheres...

{artanh} x={\frac {1}{2}}\ln \left((1+x)/(1-x)\right)} is the inverse hyperbolic tangent. This 2 arsinh {\textstyle 2\operatorname {arsinh} } formula can be...

hyperbola (/haɪˈpɜːrbələ/ ; pl. hyperbolas or hyperbolae /-liː/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in a plane, defined...

most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant...

(translation and rotation) of the hyperbolic plane. A horocycle can also be described as the limit of the circles that share a tangent at a given point, as their...

{\displaystyle \alpha } between the tangent of any curve and the tangent of its corresponding polar circle. For the hyperbolic spiral r = a φ {\displaystyle...

logarithms comes through hyperbolic sectors that are permuted by squeeze mappings while preserving their area. The area of a hyperbolic sector is taken as a...

hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder, there are several ways in...

is a circle in the Euclidean plane, in a family of circles that are all tangent to the x {\displaystyle x} -axis at rational points. For each rational...

CORDIC (Jack E. Volder), Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.)...

indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals...

to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident. The area of a regular polygon is half its...

externally tangent to the extensions of their sides). If the sizes of an inscribed and a circumscribed circle are fixed, the right kite has the largest area of...

the gnomonic projection to relate a plane σ to points on a hemisphere tangent to it. With O the center of the hemisphere, a point P in σ determines a...