By inspection, a froth of soap bubbles suggests that an infinite variety of configurations can be formed by joining soap bubbles, when actually they come together in only two ways. The possible configurations are governed by a few elementary rules that have been known for more than a century. More recently, Frederick J. Almgren, Jr., and Jean E. Taylor showed that three basic rules govern the geometry of soap bubbles and that these rules are the mathematical consequence of a simple Area-minimizing Principle.

The three basic rules are:

First, a compound soap bubble consists of flat or smoothly curved surfaces smoothly joined together.

Second, the surfaces meet in only two ways: Either exactly three (3) surfaces meet along a smooth curve (edge) or six (6) surfaces (together with four curves) meet at a vertex.

Third, when surfaces meet along curves or when curves and surfaces meet at points, they do so at equal angles. In particular, when three (3) surfaces meet along a curve, they do so at angles of 120° with respect to one another, and when four (4) curves meet at a point, they do so at angles of 109.47° (109°28'16").

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