It's been a while since I left math for industry but I once heard that the shape and contents of "the space of all problem sets and solution sets for enumerative geometry on arbitrary n-manifolds" is something that is amenable to investigation through something called Gromov-Witten theory. I did a quick number of searches on GW theory just now and cannot decipher the results so I still don't know if that claim had any merit to it but a sanity check suggests there's no obvious computational reason that it couldn't be true for n=2 or 3.
"Slide whichever circle is smaller entirely inside the bigger one, and now the answer is zero: You can’t draw any lines that touch each circle only once."
This sounds false. If the smaller circle is at the edge of the larger one, it is still entirely inside the larger one while a tangent line could touch both of them at the edge.
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[ 35.6 ms ] story [ 465 ms ] threadNot a proof but just something visual I noticed.
This sounds false. If the smaller circle is at the edge of the larger one, it is still entirely inside the larger one while a tangent line could touch both of them at the edge.