Soap bubbles and minimal surfaces
Virginia Aguilera Gómez
INDEX
- What is it?
- How does it work?
- Joseph Plateau
- Where is it on Matemápolis?
- Experiment
- Bibliography
What is it?
A bubble has the smallest surface possible. That’s why they recieved the name of minimal surfaces. They are called that way because they minimalize the surface for a determined volume. A bubble has the capacity to form a thin layer catching the air. That’s why they use the tension can influence a lot. Minimal surfaces are a two-dimensional element that locally minimizes its area. This is equivalent to having zero mean curvature. Physical models of surfaces that minimize an area can be visualized by introducing a wire frame into a soap solution, then forming a soap film, forming a minimal surface whose boundary is the wire frame.
How does it work?
A thin film of soap is formed by a thin layer of water trapped between two layers of surfactant molecules, in this case soap. The shape is determined by surface tension, a property that liquids have, which is like an energy necessary for cohesion between molecules. The mean curvature is a measure of how much the normal vector to the surface changes when we move slightly along the surface, that is, how curved the surface is in a point.
Joseph Plateau
Joseph-Antoine Ferdinand Plateau was a Belgian physicist who defined the principle of the persistence of vision in 1829. He's know becayse he created the Plateau's Problem, which tried to show the existence of a minimal surface with a given boundary. The question is: Which is the surface of rotation that has the smallest possible area?
Where is it?
Bibliography
- https://www.ucm.es/data/cont/docs/76-2013-06-11-02_Surface_tension_and_soap_films.pdf
- https://es.wikipedia.org/wiki/Problema_de_Plateau
- https://es.wikipedia.org/wiki/Joseph-Antoine_Ferdinand_Plateau
Thank you
Soap bubbles and minimal surfaces
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Transcript
Soap bubbles and minimal surfaces
Virginia Aguilera Gómez
INDEX
What is it?
A bubble has the smallest surface possible. That’s why they recieved the name of minimal surfaces. They are called that way because they minimalize the surface for a determined volume. A bubble has the capacity to form a thin layer catching the air. That’s why they use the tension can influence a lot. Minimal surfaces are a two-dimensional element that locally minimizes its area. This is equivalent to having zero mean curvature. Physical models of surfaces that minimize an area can be visualized by introducing a wire frame into a soap solution, then forming a soap film, forming a minimal surface whose boundary is the wire frame.
How does it work?
A thin film of soap is formed by a thin layer of water trapped between two layers of surfactant molecules, in this case soap. The shape is determined by surface tension, a property that liquids have, which is like an energy necessary for cohesion between molecules. The mean curvature is a measure of how much the normal vector to the surface changes when we move slightly along the surface, that is, how curved the surface is in a point.
Joseph Plateau
Joseph-Antoine Ferdinand Plateau was a Belgian physicist who defined the principle of the persistence of vision in 1829. He's know becayse he created the Plateau's Problem, which tried to show the existence of a minimal surface with a given boundary. The question is: Which is the surface of rotation that has the smallest possible area?
Where is it?
Bibliography
Thank you