With Dr Holly Krieger from Murray Edwards College, University of Cambridge. Have a look at Brilliant (and get 20% off) here: More Numberphile videos with Dr Krieger: Her Twitter: Extra detail via Holly: Here's a link to an article (meant for a somewhat general audience) by Bob Devaney explaining the numbers of components, which are called periods: And more from Bob: If checking out --- Try the complex algebra course at Editing and animation by Pete McPartlan Farey Sums: Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: Numberphile on Facebook: Numberphile tweets: Subscribe: Videos by Brady Haran Patreon: Brady's videos subreddit: Brady's latest videos across all channels: Sign up for (occasional) emails: