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

0 votes
1 answer
85 views

Lattice-point-free body diameter

The following interesting problem was asked at Aops and I wonder if it was based on some research paper: Let $K$ be a convex body in $\mathbb R^2$, such that the diameter of $K$ is less than $\sqrt2$ …
jack's user avatar
  • 3,153
6 votes
2 answers
361 views

Triangles whose vertices and center have all the same color

A plane is colored with two colors. It's an easy exercise to prove that it's always possible to find an equilateral triangle whose vertices have all the same color. Does anyone know any proof or re …
jack's user avatar
  • 3,153
5 votes
2 answers
306 views

Tiling a Jordan polygon

I saw this problem some years ago, don't remember the source: Let $P$ be a Jordan polygon (i.e. the only points of the plane belonging to two edges are the polygon vertices) that can be tiled with pa …
jack's user avatar
  • 3,153