#1
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Soap bubbles
Soap bubbles are physical examples of
the complex mathematical problem of minimal surface. They will assume the shape of least surface area possible containing a given volume. A true minimal surface is more properly illustrated by a soap film, which has equal pressure on inside as outside, hence is a surface with zero mean curvature. A soap bubble is a closed soap film: due to the difference in outside and inside pressure, it is a surface of constant mean curvature. Soap films are thin layers of liquid (usually water-based) surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Thus, foams are composed of a network of films connected by Plateau borders. Soap films can be used as model systems for minimal surfaces, which are widely used in mathematics. Wiki |
#2
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Mathematically, the question of what shape the soap bubble will form
is a minimization problem: the surface area seeks to be as small as possible under a constraint (the volume is constant and the boundary spans a given countour). This is known as Plateau's problem. https://brilliant.org/wiki/math-of-s...nd-honeycombs/ |
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