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The straightedge and the compass. The name is due to the fact that connecting points with segments, prolonging segments and drawing circles with a given center and a given ...

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

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 ...

The group of rotations and translations.

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

A mapping of a domain F:U->U to itself.

A hole in a mathematical object is a topological structure which prevents the object from being continuously shrunk to a point. When dealing with topological spaces, a ...

Given a Euclidean n-space, H_n=n+1.