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22 votes
1 answer
886 views

Happy ants never leave compact domain?

I am curious if the following seemingly simple question has an easy answer? Consider an ant population of $N$ ants that lives in $\mathbb R^2$. Each ant can be labeled by some coordinate $x\in \mathbb ...
10 votes
0 answers
497 views

Which finite sets could be packed into a square?

This question is inspired by an interesting visualization of the finite levels of von Neumann's hierarchy on Adam P. Goucher's blog, Complex Projective 4-Space. The problem starts with a two-...