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Jun 28, 2015 at 0:58 comment added Joseph O'Rourke This view nicely explains why the phenomenon is definitely not present in $\mathbb{R}^3$.
Jun 27, 2015 at 22:59 comment added Joseph O'Rourke Very nice description in terms of zones! All that is needed to understand this is the behavior of $r^{d-1}$. Which, as @foliations says, is the key ($t^n$ in f's version).
Jun 27, 2015 at 20:18 comment added Andreas Blass It's debatable whether my answer here is really different from the one posted by @foliations while I was writing mine, or whether it's more intuitive than a standard proof. But it uses fewer mathematical symbols and so has a chance of being verbally explainable.
Jun 27, 2015 at 20:13 history answered Andreas Blass CC BY-SA 3.0