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If x is a regular patch on a regular surface in R^3 with normal N^^, then x_(uu) = Gamma_(11)^1x_u+Gamma_(11)^2x_v+eN^^ (1) x_(uv) = Gamma_(12)^1x_u+Gamma_(12)^2x_v+fN^^ (2) ...

If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

For a form Q, the generic character chi_i(Q) of Q is defined as the values of chi_i(m) where (m,2d)=1 and Q represents m: chi_1(Q), chi_2(Q), ..., chi_r(Q) (Cohn 1980, p. ...

A triangle formed by the arcs of three geodesics on a smooth surface.

The identity PVint_(-infty)^inftyF(phi(x))dx=PVint_(-infty)^inftyF(x)dx (1) holds for any integrable function F(x) and phi(x) of the form ...

The dual of the great snub icosidodecahedron U_(57) and Wenninger dual W_(113).

One of the eight convex deltahedra built up from 16 equilateral triangles. It consists of two oppositely faced square pyramids rotated 45 degrees to each other and separated ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

The Heronian mean of two numbers a and b is defined as HM(a,b) = 1/3(2A+G) (1) = 1/3(a+sqrt(ab)+b), (2) where A is the arithmetic mean and G the geometric mean. It arises in ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...