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A regular patch is a patch x:U->R^n for which the Jacobian J(x)(u,v) has rank 2 for all (u,v) in U. A patch is said to be regular at a point (u_0,v_0) in U provided that its ...

The 2-point Newton-Cotes formula int_(x_1)^(x_2)f(x)dx=1/2h(f_1+f_2)-1/(12)h^3f^('')(xi), where f_i=f(x_i), h is the separation between the points, and xi is a point ...

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

The dot product can be defined for two vectors X and Y by X·Y=|X||Y|costheta, (1) where theta is the angle between the vectors and |X| is the norm. It follows immediately ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

Multiple edges are two or more edges connecting the same two vertices within a multigraph. Multiple edges of degree d_(ij) between vertex i and vertex j correspond to an ...

A permutation group is a finite group G whose elements are permutations of a given set and whose group operation is composition of permutations in G. Permutation groups have ...