Conoid
From Wikipedia, the free encyclopedia
For the organelle called conoid used by intracellular parasites, see myzocytosis.
The hyperbolic paraboloid z=xy is a conoid with x-axis as its axis.
The hyperbolic paraboloid z=xy is a conoid with y-axis as its axis.
In geometry, a conoid is a Catalan surface all of whose rulings intersect a fixed line, called the axis of the conoid. If all its rulings are perpendicular to its axis, then the conoid is called a right conoid.
For example, the hyperbolic paraboloid z = xy is a conoid (in fact, a right conoid) with x-axis and y-axis as its two axes.
A conoid can be represented by parametric equations
where {ℓ, m, n} is a vector parallel to the axis of the conoid and ƒ(u) is some function.
If ℓ = m = 0 and n = 1, then the conoid is a right conoid.
See also
References
- A. Gray, E. Abbena, S. Salamon,Modern differential geometry of curves and surfaces with Mathematica, 3rd ed. Boca Raton, FL:CRC Press, 2006. (ISBN 9781584884484)
- Vladimir Y. Rovenskii, Geometry of curves and surfaces with MAPLE (ISBN 978-0-8176-4074-3)
External links
- Hazewinkel, Michiel, ed. (2001), "Conoid", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
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