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Minimal surface

From Academic Kids

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Verrill_minimal_surface.jpg
Verrill Minimal Surface

In mathematics, a minimal surface is a surface with a mean curvature of zero. This includes, but is not limited to, surfaces of minimum area subject to constraints on the location of their boundary.

Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film.

Examples of minimal surfaces include catenoids and helicoids. A minimal surface made by rotating a catenary once around the axis is called a catenoid. A surface swept out by a line rotating with uniform velocity around an axis perpendicular to the line and simultaneously moving along the axis with uniform velocity is called a helicoid.

Minimal surfaces have become an area of intense mathematical and scientific study over the past 15 years, specifically in the areas of molecular engineering and materials science, due to their anticipated nanotechnology applications.

See also

soap bubble, Plateau's problem, curvature

References

  • Robert Osserman, A Survey of Minimal Surfaces, (1986) Dover Publications, New York. ISBN 0-486-64998-9 (Introductory text for surfaces in n-dimensions, including n=3; requires strong calculus abilities but no knowledge of differential geometry.)
  • Hermann Karcher and Konrad Polthier, Touching Soap Films (http://www.zib.de/polthier/booklet/intro.html) (2004) (website) (graphical introduction to minimal surfaces and soap films.)
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