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Given the statement "if P, then Q," or P=>Q, the converse is "if Q, then P." For example, the converse of "If a thing is a dog then it is a mammal" is "If a thing is a mammal ...

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

Discrete group theory is a broad subject covering certain aspects of groups. Such topics as free groups, group presentations, fundamental groups, Kleinian groups, and ...

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

An object that is not superimposable on its mirror image is said to be dissymmetric. All asymmetric objects are dissymmetric, and an object with no improper rotation ...

The surface with three cross-caps (Francis and Collins 1993, Francis and Weeks 1999).

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

Two nonsuperimposable objects which are mirror images of each other are called enantiomers. The term enantiomer is synonymous with enantiomorph. For example, the letters b ...

Two matrices A and B are equal to each other, written A=B, if they have the same dimensions m×n and the same elements a_(ij)=b_(ij) for i=1, ..., n and j=1, ..., m. ...

A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.