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Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

If equilateral triangles DeltaABE_(AB), DeltaBCE_(BC), and DeltaACE_(AC) are erected externally on the sides of any triangle DeltaABC, then their centers N_(AB), N_(BC), and ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

A mapping of random number triples to points in spherical coordinates according to theta = 2piX_n (1) phi = piX_(n+1) (2) r = sqrt(X_(n+2)) (3) in order to detect unexpected ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...