> Yeah. I'm ok with calling anything that looks weird a "paradox" (even stuff like "The Monty Hall problem"), but in this case describing the problem this way is precisely what's misleading about it: the person describing the "problem" must first pretend that there is a well defined (even though possibly not known to the less educated listener than himself) "random" way to pick 2 points on a circle, which there clearly isn't: there are different algorithms to do that, that produce different distribution, which very obviously look different when plotted, and choosing any specific algorithm/distribution makes the "paradox" disappear. So I really dislike when stuff like that is called a "paradox". It's just a way to trick the listener (or yourself) into thinking there is a problem, when there really isn't any.

It is also a good way to broach a discussion on the nature of randomness.