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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

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Areas of triangles induced by $n$ points on $\mathbb{S}^1$

Suppose we are given $n$ distinct points $x_1, \dots, x_n \in \mathbb{S}^1$ on the unit circle in $\mathbb{R}^2$. Any three points induce a triangle $\Delta(x_i, x_j, x_k)$ and a total of $\sim n^3/6$ …
Stefan Steinerberger's user avatar