Conoid

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.[1]

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

$x=v\cos u+lf(u), y=v\sin u+mf(u), z=nf(u) \,$

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

• Ruled surface
• Right conoid
• Catalan surface

References

• A. Gray, E. Abbena, S. Salamon,Modern differential geometry of curves and surfaces with Mathematica, 3rd ed. Boca Raton, FL:CRC Press, 2006. [2] (ISBN:9781584884484)
• Vladimir Y. Rovenskii, Geometry of curves and surfaces with MAPLE [3] (ISBN 978-0-8176-4074-3)

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Geometry stubs Surfaces Geometric shapes Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Conohypha Conolaelaps Look at other dictionaries: conoid — CONOÍD, Ă, conoizi, de, adj., s.n. (mat.) 1. adj. Conoidal. 2. Suprafaţă generată de o dreaptă care se menţine paralelă cu un plan dat şi se sprijină pe o dreaptă fixă şi pe o curbă fixă. – Din fr. conoïde. Trimis de LauraGellner, 30.07.2004.… …   Dicționar Român Conoid — Co noid (k[=o] noid), n. [Gr. kwnoeidh s conical; kw^nos cone + e i^dos form: cf. F. cono[ i]de.] 1. Anything that has a form resembling that of a cone. [1913 Webster] 2. (Geom.) (a) A solid formed by the revolution of a conic section about its… …   The Collaborative International Dictionary of English Conoid — Co noid a. Resembling a cone; conoidal. [1913 Webster] …   The Collaborative International Dictionary of English Conoīd — (Conoides, Math.), Körper, der durch Umdrehung einer krummen Linie um eine Achse entsteht, wenn die Linie diese Achse schneidet u. ihre auf der Achse senkrechten Ordinaten mit ihrem Abstande von jenem Schneidungspunkte immerfort zunehmen. Der… …   Pierer's Universal-Lexikon Conoïd — Conoïd, in der Mathematik ein durch Umdrehung des Kegelschnitts um seine Axe gebildeter Körper …   Herders Conversations-Lexikon conoid — [kō′noid΄] adj. [Gr kōnoeidēs: see CONE & OID] cone shaped: also conoidal n. 1. a cone shaped thing 2. Geom. a solid described by a conic section revolving about its axis …   English World dictionary conoid — or conoidal adjective Date: 1570 shaped like or nearly like a cone < conoid shells > < conoid pottery > • conoid noun …   New Collegiate Dictionary conoid — 1. A cone shaped structure. 2. Part of the apical complex characteristic of the protozoan subphylum, Apicomplexa; seen in sporozoites, merozoites, or other developmental stages of sporozoans, less well developed in the piroplasms (families… …   Medical dictionary conoid — [ kəʊnɔɪd] adjective (also conoidal) chiefly Zoology approximately conical in shape. noun a conoid object …   English new terms dictionary conoid ligament — n the posterior fasciculus of the coracoclavicular ligament connecting the conoid tubercle and the base of the coracoid * * * ligamentum conoideum …   Medical dictionary 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”