Wallis's conical edge

Figure 1. Wallis's Conical Edge with

a = b = c = 1

Figure 2. Wallis's Conical Edge with

a = 1.01

,

b = c = 1

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}}

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]

References

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

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