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Featuring James Grime... Check out Jane Street's "Puzzle Page" for great brain teasers https://www.janestreet.com/puzzles/archive/ (episode sponsor) More links & stuff in full description below ↓↓↓ This video features Dr James Grime: https://www.singingbanana.com His YouTube channel: https://www.youtube.com/user/singingbanana More James on Numberphile: http://bit.ly/grimevideos Some papers about the Goat Problem... Return of the Grazing Goat in n Dimensions: https://www.jstor.org/stable/2686558 A Closed-Form Solution to the Geometric Goat Problem: https://doi.org/10.1007/s00283-020-09966-0 The Grazing Goat in n Dimensions: https://www.tandfonline.com/doi/abs/10.1080/00494925.1984.11972761 Numberphile is supported by the Simons Laufer Mathematical Sciences Institute (formerly 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 The Akamai Foundation - dedicated to encouraging the next generation of technology innovators and equitable access to STEM education - https://www.akamai.com/company/corporate-responsibility/akamai-foundation 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 Animation by Pete McPartlan With thanks to our checkers, including János Pallagi Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile 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