Plateau conjecture
Quick Summary
The Plateau conjecture, a significant development in the mathematics of minimal surfaces, was mathematically derived in 1976 by Jean Taylor and Frederick Almgren. This conjecture, stemming from the broader Plateau problem, addresses the angles formed where multiple soap films meet.1
The Plateau problem itself, first posed by Leonhard Euler and Joseph-Louis Lagrange in 1760, seeks to find the surface with the minimal area enclosed by a given curve in three dimensions. This is related to the principle that surface tension is proportional to area, meaning energy-minimizing surfaces are sought. A famous physical example is a soap bubble, which forms a sphere because a sphere has the smallest surface area for a given volume.1
The Plateau conjecture specifically states that when several soap films join, the angles at which they meet are either 120 degrees (for three films) or approximately 108 degrees (for four films). This conjecture was based on Joseph Plateau's experimental observations.1
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