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A topologically invariant property of a surface defined as the largest number of nonintersecting simple closed curves that can be drawn on the surface without separating it. ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A board covered by a lattice of pegs around which one can span rubber bands to form segments and polygons. It was invented by the Egyptian mathematician and pedagogist Caleb ...

An authalic latitude given by phi_g=tan^(-1)[(1-e^2)tanphi]. (1) The series expansion is phi_g=phi-e_2sin(2phi)+1/2e_2^2sin(4phi)+1/3e_2^3sin(6phi)+..., (2) where ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.

A type of flow technically defined in terms of the tangent bundle of a manifold.

A geodesic mapping f:M->N between two Riemannian manifolds is a diffeomorphism sending geodesics of M into geodesics of N, whose inverse also sends geodesics to geodesics ...