What Does Soap Know About Mathematics?
Noah Fang
Award: Top 100
School: international school
Teacher: wesley hung
Category: Contrived
Photo #21235
What Does Soap Know About Mathematics?
The geometry of every bit of foam ever created is defined by Plateau's Laws. Named after Belgian physicist Joseph Plateau, these three laws are the result of a simple physics phenomenon: soap films always seek the configuration of minimum surface area.
Each vertex will always have four edges, at the tetrahedral angle of approximately 109.47 degrees. No exceptions exist anywhere in nature, which each and every junction visible in this photograph obeying this rule, across the entire structure, near instantaneously.
The reason is surface tension, the same molecular force which lets water striders walk on water. Each bit of film pulls equally in their direction along its surface. This creates a balance where the junction meets at 120 degrees. Any other angle creates a force that immediately would return it to the equilibrium.
Here, the foam is solving an optimization problem: to minimize the total surface area across every cell. In mathematics, this was first formalized as the Calculus of Variations. With complex formulas and advanced mathematics concepts, these equations can take time to solve. The foam using physics can solve it in milliseconds.
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