# Minimal Surfaces and Frei Otto’s Olympic Stadium Roof

A Deep Dive into Frei Paul Otto's Innovative Approach and the Minimal Surfaces Principal.

The natural world adheres to the principle of least action, guiding the pursuit of variations in calculations to uncover the minimum action or energy. First and foremost, what do calculations of variations entail? Imagine a thread with fixed endpoints (though it need not have fixed endpoints; I used this for simplicity). We can then move that thread in any direction, and different situations result in various variations. Mathematically, we can compute the energy contained in these situations. This same concept extends to surfaces, with surfaces possessing the minimum energy being termed Minimal Surfaces. An easy example to observe is soap bubbles.

Frei Paul Otto, a German architect and structural engineer, was fervently dedicated and specialized in lightweight tensile structures. Here, a tensile structure denotes a construction of elements carrying only tension and no compression or bending. A simple suspended bridge serves as a prime example of a tensile structure.

The decision was made to host the Summer Olympics in Munich in 1972. The design of the Olympic stadium was primarily overseen by two German architects, Günther Behnishch and Frei Otto, with the assistance of John Argyris. It was Frei Otto's groundbreaking idea to construct a lightweight tent, an innovation for its time. This encompassed large sweeping canopies of acrylic glass stabilized by steel cables, employed on a large scale for the first time. Otto developed sections of the roof using the trial-and-error principle, creating large models of the roof construction, while Wolf Andrä and Fritz Leonhardt (German structural engineer) developed the roof with a CAD program elsewhere. Under the guidance of Civil engineer Jörg Schlaich, the roof over the stadium was completed on April 21, 1972.

Now, the question is: Why is this roof so crucial, and how is it lightweight? This roof essentially adheres to the principle of minimal surfaces to achieve the property of the least area. If one disregards gravity, these roofs assume the form of gigantic soap films. No other roofs could be constructed with a similar shape but a smaller surface area, consequently reducing the amount of material and, in turn, the roof's weight to a minimum. Simultaneously, balanced surface tension stabilizes the entire construction, as the tension is in equilibrium at each point on the roof, akin to a soap bubble.

Read: __Frei Otto,__ __Touching Soap Films,__ __Munich Olympic Stadium__