Plücker’s conoid

Plücker’s conoid is a ruled surfaceMathworldPlanetmath 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 wedgeMathworldPlanetmath, or a conocuneus of Wallis or even a cylindroid.

The Cartesian equation for a conoid with two folds is z=x2-y2x2+y2. This can be generalized to any desired number n of folds as x(r,θ)=rcosθ, y(r,θ)=rsinθ and z(r,θ)=csin(nθ). Plücker’s conoid has applications in mechanical drafting.


  • 1 J. Plücker, “On a new geometryMathworldPlanetmath 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