Wallis's conical edge

Right conoid ruled surface

In geometry, Wallis's conical edge is a ruled surface given by the parametric equations

x=v\cos u,\quad y=v\sin u,\quad z=c{\sqrt {a^{2}-b^{2}\cos ^{2}u}}

{\displaystyle x=v\cos u,\quad y=v\sin u,\quad z=c{\sqrt {a^{2}-b^{2}\cos ^{2}u}}}

where a, b and c are constants.

Wallis's conical edge is also a kind of right conoid. It is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections.^[1]

Figure 2. Wallis's Conical Edge with a = 1.01, b = c = 1

Figure 1. Wallis's Conical Edge with a = b = c = 1

References

A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica, 3rd ed. Boca Raton, Florida:CRC Press, 2006. [1] (ISBN 978-1-58488-448-4)