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A surface of revolution which is generalization of the ring torus. It is produced by rotating an ellipse having horizontal semi-axis a, vertical semi-axis b, embedded in the ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

A volume element is the differential element dV whose volume integral over some range in a given coordinate system gives the volume of a solid, V=intintint_(G)dxdydz. (1) In ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

Scherk's two minimal surfaces were discovered by Scherk in 1834. They were the first new surfaces discovered since Meusnier in 1776. Beautiful images of wood sculptures of ...

A (finite, circular) conical surface is a ruled surface created by fixing one end of a line segment at a point (known as the vertex or apex of the cone) and sweeping the ...

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...