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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
32
votes
Is it possible to partition $\mathbb R^3$ into unit circles?
Péter's proof is very clever and, while there is no real need to resurrect this thread, the following is quite straightforward in case one is not inclined to hunt for it in the literature on this subj …
3
votes
Classification of surfaces composed of circles
I recently spent an unhealthy amount of time thinking about whether or not you can cover R3 with circles. Turns out you can. For your own search it might be worth looking at Szulkin, Andrzej, 'R 3 is …