Right conoid

In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the axis of the right conoid.

A right conoid as a ruled surface.

Using a Cartesian coordinate system in three-dimensional space, if we take the z-axis to be the axis of a right conoid, then the right conoid can be represented by the parametric equations:

where h(u) is some function for representing the height of the moving line.

ExamplesEdit

 
Generation of a typical right conoid

A typical example of right conoids is given by the parametric equations

 

The image on the right shows how the coplanar lines generate the right conoid.

Other right conoids include:

  • Helicoid:  
  • Whitney umbrella:  
  • Wallis's conical edge:  
  • Plücker's conoid:  
  • hyperbolic paraboloid:   (with x-axis and y-axis as its axes).

See alsoEdit

External linksEdit

  • "Conoid", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
  • Right Conoid from MathWorld.
  • Plücker's conoid from MathWorld