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The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

The surface generated by a twisted curve C when rotated about a fixed axis A and, at the same time, displaced parallel to A so that the velocity of displacement is always ...

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

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 generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

A substitution which can be used to transform integrals involving square roots into a more tractable form. form substitution sqrt(x^2+a^2) x=asinhu sqrt(x^2-a^2) x=acoshu

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 ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...

S_n(z) = zj_n(z)=sqrt((piz)/2)J_(n+1/2)(z) (1) C_n(z) = -zn_n(z)=-sqrt((piz)/2)N_(n+1/2)(z), (2) where j_n(z) and n_n(z) are spherical Bessel functions of the first and ...