I like this math fact! The tip of the iceberg for a lot of cool number theory stuff. If I were asked to prove the pi/4 part, I would probably look at the analytic class number formula. I’m not sure exactly where pi/4 comes from, but that looks like the central value of a Dirichlet L-function. Is there some instinctive reason why pi/4 seems to come up more often than pi? If you multiply all of these fractions together you get pi/4. Take all of the prime numbers and for each one write it as a fraction: prime/(nearest multiple of 4). I’d have to say the following formula for pi. What’s your favourite maths-based fun fact? Thank you! I loved your videos with Brady about the Navier-Stokes equations – cool tattoos too! I can’t speak for Philosophy, but for Maths we have a set of problems that some colleges send to incoming students here: I’d start there and see how you get on. Hey! I’ve recently obtained a place at Oxford to study maths & philosophy, what would you say the best prep would be that I could do in quarantine?Ĭongratulations!! I hope to see you around next year. This is not too far from the kind of ideas that are present with Banach Tarski (or at least how I think about them). It is equal to absolutely anything you want by just taking the limit in a different way. To get a feel for how weird infinity is, just take the simple example of 0/0. I would agree very much with the idea that infinite chains of transformations aren’t possible in the real world. The gist of banach tarski is thst certain infinite chains of transformations don’t preserve volume, it has no basis in the real world because things aren’t infinitely divisable in reality. I was wondering if you could explain whether or not I’m correct in my thinking.īanach Tarski absolutely holds with a frame of reference, that is after all, all that co ordinates systems are! There by ruining the methodology that allows the paradox to occur. However i was shown a 3-dimensional visual and in that context i don’t believe the paradox would hold true because of the nature of up/down/left/right requires a frame of reference. Basically that the sum of all parts is greater than the whole. The paradox is that you could make duplicates of equal size to the original by separating the data sets by direction. I have a question about the Banach-Tarksi paradox. Hi all! I’ll be here throughout the day answering any questions you have about maths – whether related to disease modelling or not – and I’ll try my very best to explain things as simply as possible.
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