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In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

Number Theory

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

Let Gamma(z) be the gamma function and n!! denote a double factorial, then [(Gamma(m+1/2))/(Gamma(m))]^2[1/m+(1/2)^21/(m+1)+((1·3)/(2·4))^21/(m+2)+...]_()_(n) ...

A column-convex self-avoiding polygon which contains the bottom edge of its minimal bounding rectangle. The anisotropic perimeter and area generating function ...

A condition in numerical equation solving which states that, given a space discretization, a time step bigger than some computable quantity should not be taken. The condition ...

A real function is said to be differentiable at a point if its derivative exists at that point. The notion of differentiability can also be extended to complex functions ...

The directional derivative del _(u)f(x_0,y_0,z_0) is the rate at which the function f(x,y,z) changes at a point (x_0,y_0,z_0) in the direction u. It is a vector form of the ...