Triangulations

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Triangulations are rigid. You can do better using pseudo-triangles

Summary

The article explains how mathematicians discovered that ordinary triangulations, although famous for creating strong and rigid structures (like bridges and frameworks), are not the most efficient way to build rigid shapes. A better solution comes from pseudo-triangulations, where the sides of a “triangle” can be made of chains of segments instead of straight lines. These shapes can achieve the same rigidity while using fewer connections, making structures lighter and more flexible in design. 

The key idea is that certain pointed pseudo-triangulations are not only rigid but also use the minimum possible number of edges, connecting geometry, graph theory, and applications such as robotics and computational geometry. In a sense, they show that nature does not always need the simplest shapes to create strong structures — sometimes a clever variation of a familiar idea works even better.

ARTICLE