Pi hiding in prime regularities
A story of pi, prime numbers, and complex numbers, and how number theory braids them together. Check out Remix careers: https://www.remix.com/jobs The ...
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This is a video I’ve been excited to make for a while. The story here braids together prime numbers, complex numbers and pi in a very pleasing trio. Quite often in modern math, especially that which flirts with the Riemann zeta function, these three seemingly unrelated objects show up in unison, and I want to give you a peek at one instance where this happens; one of the few that doesn’t require too heavy a technical background. That’s not to say it’s easy –in fact this is one of the most intricate videos I’ve ever done– but the culmination is worth it. What we’ll end up with is a formula for pi, a certain alternating infinite sum. This formula is actually written on the mug I’m drinking coffee from as I write this, and a fun but almost certainly apocryphal story is that the b...
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This is a video I’ve been excited to make for a while. The story here braids together prime numbers, complex numbers and pi in a very pleasing trio. Quite often in modern math, especially that which flirts with the Riemann zeta function, these three seemingly unrelated objects show up in unison, and I want to give you a peek at one instance where this happens; one of the few that doesn’t require too heavy a technical background. That’s not to say it’s easy –in fact this is one of the most intricate videos I’ve ever done– but the culmination is worth it. What we’ll end up with is a formula for pi, a certain alternating infinite sum. This formula is actually written on the mug I’m drinking coffee from as I write this, and a fun but almost certainly apocryphal story is that the b...
