Vi Hart discusses the paradox presented one of my previous posts, Troll Math. She explains this better than anything I’ve read so far. Measure theory and the oddities of infinity nicely wrap up this apparent contradiction.

matthen:

Given n identical circles, the problem is to find the smallest circle they can all fit into. For n up to 10, the exact answers are known- and this animation shows the best known solutions up to 50 circles. [circle packing] [code & more]

matthen:

Given n identical circles, the problem is to find the smallest circle they can all fit into. For n up to 10, the exact answers are known- and this animation shows the best known solutions up to 50 circles. [circle packing] [code & more]

Vi Hart advocates for using τ (tau) instead of 2π