9716

Jorge-Meeks K-Noids

Discovered in 1983, the Jorge and Meeks -noids are complete minimal surfaces of finite total curvature, topologically equivalent to spheres with points removed, positioned with -fold symmetry. The 2-noid is effectively a catenoid and the 3-noid is also known as the trinoid; the -noids are generalizations of the catenoid.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] L. P. Jorge and W. H. Meeks III, "The Topology of Complete Minimal Surfaces of Finite Total Gaussian Curvature," Topology, 22(2), 1983 pp. 203–221.
[2] M. Weber. "Jorge-Meeks k-Noids." Minimal Surface Archive. (Sep 2013) www.indiana.edu/~minimal/archive/Spheres/Noids/Jorge-Meeks/web/index.html.
[3] H. Karcher, "Construction of Minimal Surfaces," presentation given at Surveys in Geometry (1989), University of Tokyo, 1989. www.math.uni-bonn.de/people/karcher/karcherTokyo.pdf.
[4] U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal Surfaces, 2nd ed., New York: Springer, 2010.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+