The latest Numberphile video is a beautiful proof of Ptolemy’s Theorem, presented by Zvezdelina Stankova.

Featuring Zvezdelina Stankova... Want more? Part 2 (bringing in Pentagons and the Golden Ratio) is at: https://youtu.be/o3QBgkQi_HA More links & stuff in full description below ↓↓↓ Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos Zvezda's webpage: https://math.berkeley.edu/~stankova/ Epic Circles: https://youtu.be/sG_6nlMZ8f4 Triangle Magic Highway: https://youtu.be/wVH4MS6v23U Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

Zvezda’s proof was followed by a second video, which utilises Ptolemy’s Theorem to show two remarkable things about equilateral triangles and pentagons - well worth a look and a much shorter video.

Continuing on from Zvezda's previous video about Ptolemey's Theorem (see: https://youtu.be/bJOuzqu3MUQ) now we use it to prove some cool stuff with pentagons and equilateral triangles.

There is a third video, posted to the Numberphile2 extra channel, which shows a little bit more about the method of inversion.

Main video: https://youtu.be/bJOuzqu3MUQ See also: https://youtu.be/o3QBgkQi_HA Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos Zvezda's webpage: https://math.berkeley.edu/~stankova/ Epic Circles: https://youtu.be/sG_6nlMZ8f4 Triangle Magic Highway: https://youtu.be/wVH4MS6v23U NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Additional editing and animation by Pete McPartlan Support us on Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ A run-down of Brady's channels: http://www.bradyharan.com Sign up for (occasional) emails: http://eepurl.com/YdjL9

PS: The first video’s length and “epic-ness” is perhaps matched only by our “Epic CIrcles” from 2014, which funnily enough also heavily featured the use of inversion. That video was presented by Simon Pampena.

The man who loved circles (Objectivity): https://youtu.be/AzmUCL1OHhs More links & stuff in full description below ↓↓↓ Pappus chains, circle inversion and a whole lot more in this EPIC video with Simon Pampena.