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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Ratio of inscribed/circumscribed ellipsoids: geometrical proof?

Let $S$ be a regular simplex with vertices $x_0,\dots,x_n$ and center $c$, and let $S’$ be the simplex with vertices $c,x_1,\dots,x_n$. Let $c’$ be the center of their shared facet $x_1,\dots,x_n$. Si …
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