Who examined soap films leading him to formulate the concept of a minimal surface?

Who examined soap films leading him to formulate the concept of a minimal surface?

In 1744 Euler discovered the catenoid, the first non-planar minimal surface. This surface is readily realised by a soap film, spanning coaxial circular bounding wires. The film shrinks under the action of its surface tension, forming the minimal surface (Fig. 1.13).

What is minimal surface area?

In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term “minimal surface” is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint.

What is minimal surface architecture?

Minimal surfaces are the surfaces of the smallest area spanned by a given boundary. The equivalent is the definition that it is the surface of vanishing mean curvature. Minimal area property makes this surface suitable for application in architecture.

Who formulated the mathematical problem of the existence of minimal surface?

J.L. Lagrange
The problem of finding a minimal surface with a given boundary Γ. The problem was first formulated by J.L. Lagrange (1760), who reduced it for the class of surfaces of the form z=z(x,y) to the solution of the Euler–Lagrange equation for a minimal surface.

What is meant by soap film?

Soap films are thin layers of liquid (usually water-based) surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Soap films can be used as model systems for minimal surfaces, which are widely used in mathematics.

What is TPMS structure?

Triply Periodic Minimal Surfaces (TPMS) are a category of lattice structures that are inspired by nature. Using mathematical equations, you can control these complex structures to generate aesthetically pleasing designs with unique performance.

Are planes minimal surface?

A plane is a trivial minimal surface, and the first nontrivial examples (the catenoid and helicoid) were found by Meusnier in 1776 (Meusnier 1785). Euler proved that a minimal surface is planar iff its Gaussian curvature is zero at every point so that it is locally saddle-shaped.

What shape has smallest surface area?

sphere
Of all the shapes, a sphere has the smallest surface area for a volume. Or put another way it can contain the greatest volume for a fixed surface area. Example: if you blow up a balloon it naturally forms a sphere because it is trying to hold as much air as possible with as small a surface as possible.

Which curve gives the minimum surface of revolution?

Catenoid solution In this case, the optimal curve will necessarily be a catenary. The axis of revolution is the directrix of the catenary, and the minimal surface of revolution will thus be a catenoid.

What is soap surface tension?

Our measurements show that a soap film has a surface tension of 30 mN/m if its thickness is relatively thick or if it is made of soap solutions of higher concentrations. Otherwise, the surface tension deviates from the asymptotic value 30 mN/m and increases.

What causes soap film?

Hard water can contribute to soap scum buildup because it contains mineral salts. Therefore, soap scum forms when wet bar soap interacts with the minerals in your tap water. These minerals combine with the diluted bath soap to form a film or scum that sticks to surfaces.