Plücker’s conoid

Plücker’s conoid is a ruled surface that results from taking a straight line connected to an axis, rotating it about that axis and moving it straight up and down the axis to give the desired number of folds. Being an example of a right conoid, Plücker’s conoid is sometimes called a conical wedge, or a conocuneus of Wallis or even a cylindroid.

The Cartesian equation for a conoid with two folds is $z=\frac{x^{2}-y^{2}}{x^{2}+y^{2}}$ . This can be generalized to any desired number $n$ of folds as $x(r,\theta)=r\cos\theta$ , $y(r,\theta)=r\sin\theta$ and $z(r,\theta)=c\sin(n\theta)$ . Plücker’s conoid has applications in mechanical drafting.

References

1 J. Plücker, “On a new geometry of space”, Philosophical Transactions of the Royal Society of London 155 (1965): 725 - 791
2 S. P. Radzevich, “A Possibility of Application of Pliicker’s Conoid for Mathematical Modeling of Contact of Two Smooth Regular Surfaces in the First Order of Tangency”, Mathematical and Computer Modelling 42 (2005): 999 - 1022

Title	Plücker’s conoid
Canonical name	PluckersConoid
Date of creation	2013-03-22 16:44:02
Last modified on	2013-03-22 16:44:02
Owner	Mravinci (12996)
Last modified by	Mravinci (12996)
Numerical id	4
Author	Mravinci (12996)
Entry type	Definition
Classification	msc 51M04
Classification	msc 51M20
Classification	msc 14J25
Synonym	Plucker’s conoid
Synonym	Plücker conoid
Synonym	Plucker conoid
Synonym	conical wedge
Synonym	conocuneus of Wallis
Synonym	Wallis conocuneus