Science

# Joseph Plateau's soapy observations first defined "patterns in nature"

The laws described by this Belgian physicist are still used in geometry today.

Joseph Antoine Ferdinand Plateau, the subject of Monday’s Google Doodle, was a man of art, science, and invention. Plateau’s interests led him in a variety of directions, from the more whimsical creation of a moving picture device called the phénakistiscope, — as highlighted in the doodle today — to his deeper ruminations on the nature of the physical world.

A physicist first and foremost, Plateau is also remembered for his contributions to our understanding of one of the world’s most delicate and mysterious geometries: the soap bubble.

While soap bubbles may appear unassuming, Plateau thought they were, in fact, marvels because they almost unanimously form perfectly taut, spherical shapes with each occurrence, according to a Medium post about the discoveries..

Plateau was fascinated by this phenomena and pursued it in a series of experiments between 1842 and 1868, first in an oil “bubble” suspended in a water and alcohol solution, then in a bubble wand-like experiment in which sphere-shaped wire figures were dipped into a solution of soap and liquid glycerol before being raised to form thin, bubbly membranes.

If this is starting to sound familiar it might be because such bubble experiments are often a mainstay of nearly all children’s museums, and you’ve probably soaked your sneakers in bubble solution at some point in the past trying to recreate Plateau’s experiments.

From his numerous observations and 80-odd bubble contraptions, Plateau came to some universal conclusions about bubble membranes and what they represented in terms of something mathematicians call minimal surfaces — surfaces that naturally assume low surface energies and tensions to maintain their thin surface areas.

In the case of a soap bubble, this also means that the surface has the smallest possible area that can contain the volume of the sphere.

## Plateau’s Laws on Minimal Surface Geometries (aka soap bubbles)

1. Soap films are made of components that are smooth surfaces.
2. The mean curvature of each component of a soap film is constant.
3. Soap films connect in threes, along curves meeting at angles arccos(−1/2) = 120°.
4. These curves meet in groups of four, at vertices with angles arccos(−1/3) ≈ 109.5°.

The implications of Plateau’s research on soap bubbles and in turn minimal surfaces goes far beyond sheer curiosity — although that may be what sparked it — and has found its place in computer graphics, theoretical mathematics, and architecture, as well as in the natural world in various forms of natural incarnations.

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