Particle physics experiments: Difference between revisions

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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.]]
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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]]

Latest revision as of 06:43, 11 January 2015

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