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Cayley's cubic surface is the unique cubic surface having four ordinary double points (Hunt), the maximum possible for cubic surface (Endraß). The Cayley cubic is invariant ...

In affine three-space the Cayley surface is given by x_3=x_1x_2-1/3x_1^3 (1) (Nomizu and Sasaki 1994). The surface has been generalized by Eastwood and Ezhov (2000) to ...

There are several equivalent definitions of a closed set. Let S be a subset of a metric space. A set S is closed if 1. The complement of S is an open set, 2. S is its own set ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

The complex structure of a point x=x_1,x_2 in the plane is defined by the linear map J:R^2->R^2 J(x_1,x_2)=(-x_2,x_1), (1) and corresponds to a counterclockwise rotation by ...

A concho-spiral, also known as a conchospiral, is a space curve with parametric equations r = mu^ua (1) theta = u (2) z = mu^uc, (3) where mu, a, and c are fixed parameters. ...

A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...