In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder.
Plücker's conoid is the surface defined by the function of two variables:
This function has an essential singularity at the origin.
By using cylindrical coordinates in space, we can write the above function into parametric equations
Thus Plücker's conoid is a right conoid, which can be obtained by rotating a horizontal line about the with the oscillatory motion (with period 2π) along the segment of the axis (Figure 4).
A generalization of Plücker's conoid is given by the parametric equations
where denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the is . (Figure 5 for )
See also Ruled surface Right conoid Wallis's conical edge
References A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica, 3rd ed. Boca Raton, Florida:CRC Press, 2006. () Vladimir Y. Rovenskii, Geometry of curves and surfaces with MAPLE ()
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