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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

1 vote

A randomized version of straight-edge and compass construction

Fleshing out my comment slightly, here's a heuristic argument with a couple of blanks to be filled in that suggests that most points will be 'found' with probability $\lt 1$. For approximation purpose …
Steven Stadnicki's user avatar
1 vote

Geometric probabilistic problem on triangles on a plane

A bit too long for a comment, here's one suggestion: take $a\lt b\lt c$ and use $(0,0)$ and $(c,0)$ as two points of the triangle. The third point $(x,y)$ (taking $y\gt 0$ WLOG) can be found in whatev …
Steven Stadnicki's user avatar
5 votes

Which unfoldings of the hypercube tile 3-space: How to check for isometric space-fillers?

For your first question, I haven't gone through all of the unfoldings, but the first one there clearly tiles space: it even tiles a 2-cell thick infinite plane (which can then be stacked to tile space …
Steven Stadnicki's user avatar