Associated Surface of a Minimal Möbius Strip
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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 , 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 .
Contributed by: Enrique Zeleny (June 2014)
Open content licensed under CC BY-NC-SA
Starting with a circle , we construct a winding normal that is . Using the Björling formula with these curves, we obtain the minimal Möbius strip
 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.
 H. Gollek. "Natural Equations and Deformations of Minimal Curves." (Jun 20, 2014) www-irm.mathematik.hu-berlin.de/~gollek/MinSurfs/min.ps.