Pi hiding in prime regularities

A story of pi, primes, complex numbers, and how number theory braids them together. Mathologer on why 4k 1primes break down as sums of squares: Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: Home page: For those of you curious about the finer details, here’s a writeup from the viewer Daniel Flores justifying the final approximation: The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as “Fermat’s theorem on sums of two squares“: Music by Vince Rubinetti: Timestamps 0:00 - Introduction 1:39 - Counting lattice points 5:47 - Gaussian integers 10:30 - The lattice point recipe 17:50 - Counting on one ring 20:14 - Exploiting prime regularity 25:19 - Combining the rings 28:36 - Branches of number theory ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you’re into that). If you are new to this channel and want to see more, a good place to start is this playlist: Various social media stuffs: Website: Twitter: Patreon: Facebook: Reddit: