Right conoid

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A right conoid as a ruled surface.

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.

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.

Examples[edit]

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 also[edit]

External links[edit]

  • Hazewinkel, Michiel, ed. (2001) [1994], "Conoid", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
  • Right Conoid from MathWorld.
  • Plücker's conoid from MathWorld