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The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

The Kummer surfaces are a family of quartic surfaces given by the algebraic equation (x^2+y^2+z^2-mu^2w^2)^2-lambdapqrs=0, (1) where lambda=(3mu^2-1)/(3-mu^2), (2) p, q, r, ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

Complex Analysis