Dini's surface

Dini's surface
Dini's surface with 0 ≤ u ≤ 4π 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.[1] It is named after Ulisse Dini[2] and described by the following parametric equations:[3]

x=a\cos\left(u\right)\sin\left(v\right)
y=a\sin\left(u\right)\sin\left(v\right)
z=a\left(\cos\left(v\right)+\log\left(\tan\left(\frac{v}{2}\right)\right)\right)+bu

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

  1. ^ "Wolfram Mathworld: Dini's Surface". http://mathworld.wolfram.com/DinisSurface.html. Retrieved 2009-11-12. 
  2. ^ J J O'Connor and E F Robertson (2000). "Ulisse Dini Biography". School of Mathematics and Statistics, University of St Andrews, Scotland. http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Dini.html. Retrieved 209-11-14. 
  3. ^ "Knol: Dini's Surface (geometry)". http://knol.google.com/k/suresh-emre/dini-s-surface-geometry/35vsnxisjn2mw/26#. Retrieved 2009-11-12. 
  4. ^ Rogers and Schief (2002). Bäcklund and Darboux transformations: geometry and modern applications in Soliton Theory. Cambridge University Press. pp. 35–36. 

Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Dini — may refer to: Barbana Dini, Albanian singer Dini Exams, religious exams Dino Dini, English games developer Lamberto Dini, Italian politician Mohamed Dini Farah, Djiboutian politician Muguette Dini, French politician Paul Dini, animation and comic …   Wikipedia

  • Helicoid — A helicoid with α=1, 1≤ρ≤1 and π≤θ≤π. The helicoid, after the plane and the catenoid, is the third minimal surface to be known. It was first discovered by Jean Baptiste Meusnier in 1776. Its name derives from its similarity to the helix: for… …   Wikipedia

  • Mathematica — For other uses, see Mathematica (disambiguation). Mathematica Mathema …   Wikipedia

  • Projet:Mathématiques/Liste des articles de mathématiques — Cette page n est plus mise à jour depuis l arrêt de DumZiBoT. Pour demander sa remise en service, faire une requête sur WP:RBOT Cette page recense les articles relatifs aux mathématiques, qui sont liés aux portails de mathématiques, géométrie ou… …   Wikipédia en Français

  • Djibouti — Djiboutian, adj., n. /ji booh tee/, n. 1. Formerly, French Somaliland, French Territory of the Afars and Issas. a republic in E Africa, on the Gulf of Aden: a former overseas territory of France; gained independence 1977. 434,116; 8492 sq. mi.… …   Universalium

  • Italy — /it l ee/, n. a republic in S Europe, comprising a peninsula S of the Alps, and Sicily, Sardinia, Elba, and other smaller islands: a kingdom 1870 1946. 57,534,088; 116,294 sq. mi. (301,200 sq. km). Cap.: Rome. Italian, Italia. * * * Italy… …   Universalium

  • Tour de Corse — Cet article concerne le rallye automobile. Pour la course cycliste, voir Tour de Corse cycliste. Tour de Corse …   Wikipédia en Français

  • Calendar of 1996 — ▪ 1997 JANUARY JANUARY 1       King Fahd cedes power       Still experiencing the effects of a stroke suffered in November 1995, Saudi Arabia s King Fahd, who also held the post of prime minister, ceded temporary power to Crown Prince Abdullah,… …   Universalium

  • List of He-Man and the Masters of the Universe episodes — The following is a list of episodes for the 1980s animated series He Man and the Masters of the Universe. The following is a list of episodes of the television series. (Note: the episodes are listed here in production order, which differs greatly …   Wikipedia

  • Liste des articles de mathematiques — Projet:Mathématiques/Liste des articles de mathématiques Cette page recense les articles relatifs aux mathématiques, qui sont liés aux portails de mathématiques, géométrie ou probabilités et statistiques via l un des trois bandeaux suivants  …   Wikipédia en Français

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”