10182

# Associated Surface of a Minimal Möbius Strip

This Demonstration shows a minimal version of the celebrated Möbius strip (a nonorientable surface or one-sided surface). The surface is obtained by computing a Björling curve [1], extrapolating a surface when a determined curve (in this case the circle) is known, along with a given unit normal. The associated surface shown here can be generated by means of a complex conformal transformation, simply by multiplying the minimal curve by the factor [2].

### DETAILS

Starting with a circle , we construct a winding normal that is . Using the Björling formula with these curves, we obtain the minimal Möbius strip
.
References
[1] P. Mira, "Complete Minimal Möebius Strips in and the Björling Problem," Journal of Geometry and Physics, 56(9), 2006 pp. 1506–1515. filemon.upct.es/~pmira/pdf/MobiusCTF.pdf.
[2] H. Gollek. "Natural Equations and Deformations of Minimal Curves." (Jun 20, 2014) www-irm.mathematik.hu-berlin.de/~gollek/MinSurfs/min.ps.

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.