Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
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What (who) is triply$85216$ - definition
![[[Costa's Minimal Surface]]](https://commons.wikimedia.org/wiki/Special:FilePath/Costa's Minimal Surface.png?width=200 "[[Costa's Minimal Surface]]")
![[[Saddle tower]] minimal surface. While any small change of the surface increases its area, there exist other surfaces with the same boundary with a smaller total area.](https://commons.wikimedia.org/wiki/Special:FilePath/Saddle Tower Minimal Surfaces.png?width=200 "[[Saddle tower]] minimal surface. While any small change of the surface increases its area, there exist other surfaces with the same boundary with a smaller total area.")
Wikipedia
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum.
