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The inversion of a spindle torus. If the inversion center lies on the torus, then the spindle cyclide degenerates to a parabolic spindle cyclide.

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...