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Bubble


Bubble

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More complicated forms occur when multiple bubbles are joined together. The simplest example is the double bubble, and beautiful configurations can form when three or more bubbles are conjoined (Sullivan).

An outstanding problem involving bubbles is the determination of the arrangements of bubbles with the smallest surface area which enclose and separate n given volumes in space.


See also

Double Bubble, Plateau's Laws, Plateau's Problem, Sphere

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References

Morgan, F. "Mathematicians, Including Undergraduates, Look at Soap Bubbles." Amer. Math. Monthly 101, 343-351, 1994.Pappas, T. "Mathematics & Soap Bubbles." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 219, 1989.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 214-216, 1999.Sullivan, J. M. "Generating and Rendering Four-Dimensional Polytopes." Mathematica J. 1, 76-85, Winter 1991.Sullivan, J. M. "Polytope Bubble Images." http://torus.math.uiuc.edu/jms/Images/polyt.html.Williams, R. The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover, pp. 44-45, 1979.

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Bubble

Cite this as:

Weisstein, Eric W. "Bubble." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bubble.html

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