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How to Fill a Klein Bottle - Numberphile

In a 3D world, it's possible to fill 4D Klein Bottles - featuring Cliff Stoll. More Cliff videos: http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓ More Klein Bottle videos: http://bit.ly/KleinBottles You can buy a bottle from Cliff: https://www.kleinbottle.com See our videos with the Pope's Astronomer (and good friend of Cliff) Brother Guy Consolmagno: SPACE ROCKS    • The Pope's Space Rocks - Objectivity 221   VATICAN TELESCOPES    • The Pope's Telescopes - Deep Sky Videos   THE POPE’S ASTRONOMER    • The Pope's Astronomer - Sixty Symbols   Cliff notes: Cliff advises not to rely on his memory for the volume of a sphere. It's really 4/3 π r^3. Cliff also says that using a tube to break the vapor lock is challenging. Straws (even flexo-straws) kink when bent around narrow hairpin curves. And most flexible tubes (especially aquarium air tubing) have high friction against glass, so they're difficult to thread along the curve. 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/outr... And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:   / numberphile   Numberphile tweets:   / numberphile   Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation by Pete McPartlan Patreon:   / numberphile   Numberphile T-Shirts and Merch: https://teespring.com/stores/numberphile Brady's videos subreddit:   / bradyharan   Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9