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Results tagged with convex-geometry
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user 4720
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
61
votes
Accepted
How to explain the concentration-of-measure phenomenon intuitively?
As I see it, the key intuition is passing from the equator orthogonal to a single vector to looking at a whole orthonormal basis.
Suppose we pick a random unit vector $(x_1,\dots,x_n)$. What we want …
- 16.8k
4
votes
Delaunay triangulations and convex hulls
It's known; for example, my coauthors and I used this characterization in http://arxiv.org/abs/math.MG/0611451. However, we certainly weren't the first, and I don't know the earliest reference. I th …
- 16.8k
18
votes
Accepted
Optimal 8-vertex isoperimetric polyhedron?
An $8$-vertex polyhedron can achieve an isoperimetric ratio of $A^3/V^2 = 159.3243297053\dots$, and based on some quick experiments I'm pretty confident this is optimal (although I wouldn't be shocked …
- 16.8k