Plücker's conoid
Introduction Figure 1.Plücker's conoid with .Figure 2.Plücker's conoid with .Figure 3.Plücker's conoid with .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 2''π'') 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 )Figure 4.Plücker's conoid with .Figure 5.Plücker's conoid with File:Plucker conoid (n=2).gif|Animation of Plucker's conoid with File:Plucker's conoid (n=2).jpg|Plucker's conoid with File:Plucker's conoid (n=3).jpg|Plucker's conoid with File:Plucker's conoid (n=2).gif|Animation of Plucker's conoid with File:Plucker's conoid (n=3).gif|Animation of Plucker's conoid with File:Plucker's conoid (n=4).jpg|Plucker's conoid with
See also *Ruled surface*Right conoid
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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