Dini's surface plotted with adjustable parameters by Wolfram Mathematica program
Dini's Surface with constants a = 1, b = 0.5 and 0 ≤ u ≤ 4π and 0<v<1.

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]

Dini's surface with 0 ≤ u ≤ 4π and 0.01 ≤ v ≤ 1 and constants a = 1.0 and b = 0.2.

Another description is a generalized helicoid constructed from the tractrix.[4]

See also

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References

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  1. ^ "Wolfram Mathworld: Dini's Surface". 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. Archived from the original on 2012-06-09. Retrieved 2016-04-12.
  3. ^ "Knol: Dini's Surface (geometry)". Archived from the original on 2011-07-23. 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.

📚 Artikel Terkait di Wikipedia

Pseudosphere

radius R, which is a surface of curvature 1/R2. Examples include the tractroid, Dini's surfaces, breather surfaces, and the Kuen surface. The term "pseudosphere"

List of surfaces

paraboloid (a ruled surface) Paraboloid Dini's surface Pseudosphere Cayley cubic Barth sextic Clebsch cubic Monkey saddle (saddle-like surface for 3 legs.) Torus

Dini

anti-colonial DinI-like protein family Pernikahan Dini, a soap opera that aired on RCTI in 2001 Dinis (disambiguation) Dino (disambiguation) This disambiguation

Ulisse Dini

(Pisa, T. Nistri, 1878) Dini continuity Dini criterion Dini derivative Dini series Dini test Dini's theorem Dini's surface Dini–Lipschitz criterion See

Helicoid

are locally isometric surfaces; see Catenoid#Helicoid transformation. Generalized helicoid Dini's surface Right conoid Ruled surface Catalan, Eugène (1842)

Hyperbolic space

other hyperbolic surfaces. The analogous construction for three-dimensional hyperbolic surfaces is the Kleinian model. Dini's surface Hyperbolic 3-manifold

Kuen surface

"Three Pseudospherical Surfaces, Dini Family, Kuen, Breather" (PDF). virtualmathmuseum.org. Retrieved 29 March 2025. "Kuen surface". www.mathcurve.com.

Breather surface

Bibcode:1973PhRvL..30.1262A. doi:10.1103/PhysRevLett.30.1262. Dini's surface Kuen surface Xah Lee Web - Surface Gallery Breather surface in Virtual Math Museum