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The curve formed by the intersection of a cylinder and a sphere is known as Viviani's curve. The problem of finding the lateral surface area of a cylinder of radius r ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The one-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the ...

A "squashed" spheroid for which the equatorial radius a is greater than the polar radius c, so a>c (called an oblate ellipsoid by Tietze 1965, p. 27). An oblate spheroid is a ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

The real projective plane is the closed topological manifold, denoted RP^2, that is obtained by projecting the points of a plane E from a fixed point P (not on the plane), ...

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

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 ...

Togliatti surfaces are quintic surfaces having the maximum possible number of ordinary double points (31). A related surface sometimes known as the dervish can be defined by ...

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = ...