Continuing on from Zvezda's previous video about Ptolemey's Theorem (see: https://www.youtube.com/watch?v=bJOuzqu3MUQ) now we use it to prove some cool stuff with pentagons and equilateral triangles. More links & stuff in full description below ↓↓↓ Zvezda's Numberphile playlist: http://bit.ly/zvezda_videos Zvezda's webpage: https://math.berkeley.edu/~stankova/ Golden Ratio: https://www.youtube.com/watch?v=sj8Sg8qnjOg Epic Circles: https://www.youtube.com/watch?v=sG_6nlMZ8f4 Triangle Magic Highway: https://www.youtube.com/watch?v=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. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts and Merch: null Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9