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The hyperbolic cylinder is a quadratic surface given by the equation (x^2)/(a^2)-(y^2)/(b^2)=-1. (1) It is a ruled surface. It can be given parametrically by x = asinhu (2) y ...

A hyperbolic version of the Euclidean dodecahedron. Hyperbolic three-space can be tessellated with hyperbolic dodecahedra whose intermediate dihedral angles are 60, 72, or 90 ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

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) ...

In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can ...

The hyperbolic polar sine is a function of an n-dimensional simplex in hyperbolic space. It is analogous to the polar sine of an n-dimensional simplex in elliptic or ...

A polyhedron in a hyperbolic geometry.

A hyperbolic version of the Euclidean tetrahedron.

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...