How a Hobbyist Solved a 50-Year-Old Math Problem (Einstein Tile)

Video Description

Sign up to Brilliant to receive a 30-day free trial + a 20% discount with this link! https://brilliant.org/upandatom/ Recommended course: https://brilliant.org/courses/beautiful-geometric-explorations/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collections/up-and-atom Subscribe to Up and Atom for physics, math and computer science videos https://www.youtube.com/c/upandatom For a one time donation, head over to my PayPal :) https://www.paypal.me/upandatomshows Veritasium's video on Penrose tiles https://youtu.be/48sCx-wBs34?si=xwyxvhQxhOKLutIy *A big thank you to my AMAZING PATRONS!* Jonathan Koppelman, Michael Seydel, Cy 'kkm' K'Nelson, Thorsten Auth, Chris Flynn, Tim Barnard, Izzy Ca, Tate Lyles, Millennial Glacier, Richard O McEwen Jr, Scott Ready, John H. Austin, Jr., Brian Wilkins, Thomas V Lohmeier, David Johnston, Thomas Krause, Lynn Shackelford, Ave Eva Thornton, Andrew Pann, Anne Tan, Marc-Antoine, Chris Davis, Thomas Urech, chuck zegar, David Tuman, Richard Rensman, Ben Mitchell, Steve Archer, Luna, Tyler Simms, Michael Geer, James Mahoney, Jim Felich, Fabio Manzini, Jeremy, Sam Richardson, Robin High, KiYun Roe, DONALD McLeod, Ron Hochsprung, Aria Bend, James Matheson, Kevin Anderson, Alexander230, Tim Ludwig, Alexander Del Toro Barba, Justin Smith, A. Duncan, Mark Littlehale, Tony T Flores, Dagmawi Elehu, Jeffrey Smith, Alex Hackman, bpatb, Joel Becane, Paul Barclay, 12tone, Sergey Ten, John Lakeman, Jana Christine Saout, Jeff Schwarz, Yana Chernobilsky, Louis Mashado, Michael Dean, Chris Amaris, Matt G, Dag-Erling Smørgrav, John Shioli, Todd Loreman, Yaw Mintah, Carlos Escolar, Vijay Prasad, Anthony Docimo, robert lalonde, Julian Nagel, Cassandra Durnord, Antony Birch, Paul Bunbury, David Shlapak, Kent Arimura, Phillip Rhodes, Michael Nugent, James N Smith, Roland Gibson, Joe McTee, Oleg Dats, John Spalding, Simon J. Dodd, Tang Chun, Michelle, William Toffey, Michel Speiser, Rigid Designator, James Horsley, Brian Williams, Craig Tumblison, Cameron Tacklind, 之元 丁, Kevin Chi, Lance Ahmu, Markus Lindström, Steve Watson, Dexter Scott, Potch, Indrajeet Sagar, Markus Herrmann (trekkie22), Gil Chesterton, Alipasha Sadri, Pablo de Caffe, Taylor Hornby, Mark Fisher, Emily, Colin Byrne, Nick H, Jesper de Jong, Loren Hart, Sofia Fredriksson, Phat Hoang, Spuddy, Sascha Bohemia, tesseract, Stephen Britt, KG, Hansjuerg Widmer, John Sigwald, O C, Carlos Gonzalez, Thomas Kägi, James Palermo, Chris Teubert, Fran, Wolfgang Ripken, Jeremy Bowkett, Vincent Karpinski, Nicolas Frias, Louis M, kadhonn, Moose Thompson, Rick DeWitt, Pedro Paulo Vezza Campos, S, Garrett Chomka, Rebecca Lashua, Pat Gunn, George Fletcher, RobF, Vincent Seguin, Shawn, Israel Shirk, Jesse Clark, Steven Wheeler, Philip Freeman, Jareth Arnold, Simon Barker, Lou, amcnea and Simon Dargaville. *Sources and further reading* https://arxiv.org/abs/2303.10798 https://arxiv.org/abs/2305.17743 https://cs.uwaterloo.ca/~csk/hat/ https://cs.uwaterloo.ca/~csk/spectre/ Chapters 0:00 - 0:49 Introducing a NEW SHAPE 0:49 - 2:20 Never repeating pattern 2:20 - 3:16 The 50 year old mystery 3:16 - 5:03 An amazing discovery 5:03 - 10:10 How do we know it never repeats? 10:10 - 11:40 Infinitely many ein stein tiles! 11:40 - 12:39 "Haters gonna hate" 12:39 - 15:01 An indisputable ein stein tile 15:01 - 16:04 Applications 16:04 - 17:59 Learn more about tilings Creator - Jade Tan-Holmes Script - Simon Mackenzie and Jade Tan-Holmes Animations by Tom Groenestyn Music - epidemicsound.com