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The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

A polynomial having random coefficients.

The spherical Hankel function of the first kind h_n^((1))(z) is defined by h_n^((1))(z) = sqrt(pi/(2z))H_(n+1/2)^((1))(z) (1) = j_n(z)+in_n(z), (2) where H_n^((1))(z) is the ...

The spherical Hankel function of the second kind h_n^((1))(z) is defined by h_n^((2))(z) = sqrt(pi/(2x))H_(n+1/2)^((2))(z) (1) = j_n(z)-in_n(z), (2) where H_n^((2))(z) is the ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...