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[[File:Dini's Surface.svg|thumb|350px|right|Dini's surface with 0 ≤ ''u'' ≤ 4''π'' and 0.01 ≤ ''v'' ≤ 1 and constants ''a'' = 1.0 and ''b'' = 0.2.]] | |||
In [[geometry]], '''Dini's surface''' is a [[surface]] with constant negative [[curvature]] that can be created by twisting a [[pseudosphere]].<ref>{{cite web | |||
| url = http://mathworld.wolfram.com/DinisSurface.html | |||
| title = Wolfram Mathworld: Dini's Surface | |||
| accessdate = 2009-11-12}}</ref> It is named after [[Ulisse Dini]]<ref>{{cite web | |||
| url = http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Dini.html | |||
| title = Ulisse Dini Biography | |||
| publisher = School of Mathematics and Statistics, University of St Andrews, Scotland | |||
| year = 2000 | |||
| author = J J O'Connor and E F Robertson | |||
| accessdate = 209-11-14}}</ref> and described by the following [[parametric equation]]s:<ref>{{cite web | |||
| url = http://knol.google.com/k/suresh-emre/dini-s-surface-geometry/35vsnxisjn2mw/26# | |||
| title = Knol: Dini's Surface (geometry) | |||
| accessdate = 2009-11-12}}</ref> | |||
: <math>x=a\cos\left(u\right)\sin\left(v\right)</math> | |||
: <math>y=a\sin\left(u\right)\sin\left(v\right)</math> | |||
: <math>z=a\left(\cos\left(v\right)+\ln\left(\tan\left(\frac{v}{2}\right)\right)\right)+bu</math> | |||
Another description is a [[helicoid]] constructed from the [[tractrix]].<ref>{{cite book | |||
| title = Bäcklund and Darboux transformations: geometry and modern applications in Soliton Theory | |||
| last = Rogers and Schief | |||
| publisher = Cambridge University Press | |||
| pages= 35–36 | |||
| year = 2002}}</ref> | |||
== Uses == | |||
Renditions of Dini's surface have appeared on the covers of [[Western Kentucky University]]'s ''Graduate Study in Mathematics'', [[Alfred Gray (mathematician)|Gray's]] ''Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition'', and volume 2, number 3 of ''La Gaceta de la Real Sociedad Matemática Española''. | |||
== See also == | |||
*[[Dini derivative]] | |||
*[[Dini test]] | |||
*[[Dini's theorem]] | |||
*[[List of surfaces]] | |||
== References == | |||
{{reflist}} | |||
== External links == | |||
*[http://life-graphics.com/Home/Graphic3DP/355?pId=10010 View in 3D] | |||
[[Category:Surfaces]] | |||
Revision as of 14:01, 9 July 2013
In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere.[1] It is named after Ulisse Dini[2] and described by the following parametric equations:[3]
Another description is a helicoid constructed from the tractrix.[4]
Uses
Renditions of Dini's surface have appeared on the covers of Western Kentucky University's Graduate Study in Mathematics, Gray's Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, and volume 2, number 3 of La Gaceta de la Real Sociedad Matemática Española.
See also
References
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External links
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web
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