From the wikipedia article on Primitive Recursive Arithmetic (see http://en.wikipedia.org/wiki/Primitive_recursive_arithmetic): "Primitive recursive arithmetic, or PRA, is a quantifier-free ...
(This question is inspired by Erich's Packing Center. I'm just asking about circles in squares to keep things simple, since I suspect any answer would apply just-as-well to the rest of the problems ...
Throw $n$ balls into $n$ bins and let $X_n$ be the maximum occupancy. That is the maximum number of balls found in any bin. If you throw the balls uniformly and independently it is known that ...
I'm reading the Otal's survey on the compactification of Morgan Shalen. (available here) He claims in an example (page 8) that the compactification of $\mathbb C^2$ is $S^4$, which sounds completely ...