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Results tagged with mg.metric-geometry
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user 97426
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
4
votes
Accepted
Shortcutting quasigeodesics
As suggested, I am turning my comments into an answer. The answer to both questions is negative for any $\lambda > 1$, and positive for $\lambda = 1$.
For $\lambda = 1+\epsilon$ note that in $\mathbb …
- 2,671
18
votes
Accepted
Tiling with similar tiles
Non-convex solutions to Question 1
Consider the following polygon (the outward angle on the right is the same as the inward angle at the top)
Since I didn't know any better way to show it does not ti …
- 2,671
7
votes
Tiling with similar tiles
Here is an answer to Question 2. The following shape (attributed to Karl Scherer on this website) tiles into similar shapes of different sizes.
Convincing myself that it is not a rep-tile took me sev …
- 2,671
2
votes
Accepted
Folding a non-rectangular shape into a rectangle of uniform thickness
I also have no solution for $n=3$, but I have solutions for every $n > 3$. The constructions are sketched below, for each of them we fold along all grid lines; folding along the red lines first has he …
- 2,671