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The Banach–Tarski Paradox
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The Banach–Tarski Paradox
  • Published_at:2015-08-01
  • Category:Science & Technology
  • Channel:Vsauce
  • tags: Banach–Tarski Paradox Paradox (Quotation Subject) Mathematics (Field Of Study) Alfred Tarski (Academic) Stefan Banach (Academic) math maths infinity infinite chocolate trick infinite Topology (Field Of Study) vsauce michael stevens Georg Cantor (Academic) hilbert's hotel David Hilbert (Academic) numberphile learning education lecture animation diagram visual explination
  • description: Q: "What's an anagram of Banach-Tarski?" A: "Banach-Tarski Banach-Tarski." twitter: https://www.twitter.com/tweetsauce Instagram: http://www.instagram.com/electricpants Kevin’s Field Day video: https://www.youtube.com/watch?v=1zARMZ08ums Field Day: https://www.youtube.com/channel/UCRPktNf5vnBR1J4e7t1RUVg Deep dream animation by http://instagram.com/NaderMakki/ If you like it, you'll love this video also by Nader: https://www.youtube.com/watch?v=fJ9j_z2kXI0 Chocolate illusion: http://mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/ Chocolate illusion video: https://www.youtube.com/watch?v=dmBsPgPu0Wc related Numberphile videos: sizes of infinity (includes diagonal argument): https://www.youtube.com/watch?v=elvOZm0d4H0 infinity paradoxes: https://www.youtube.com/watch?v=dDl7g_2x74Q Vi Hart on types of infinity: https://www.youtube.com/watch?v=23I5GS4JiDg Countable & uncountable definitions: http://mathinsight.org/definition/uncountable https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Uncountable_set Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Banach-Tarski proofs: http://math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf https://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf http://people.math.umass.edu/~weston/oldpapers/banach.pdf Banach-Tarski explinations online: http://www.irregularwebcomic.net/2339.html http://www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10 http://skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html http://austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html http://www.math.cornell.edu/~mec/Summer2009/Whieldon/Math_Explorers_Club%3A__Lesson_Links/Entries/2009/7/28_Lesson_6%3A__Whats_an_Anagram_of_Banach-Tarski.html http://rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf http://quibb.blogspot.co.uk/2013_03_01_archive.html http://blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html https://geopolicraticus.wordpress.com/tag/banach-tarski-paradox/ http://dgleahy.com/p47.html https://www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml Cayley graph animated gif: https://twitter.com/GIFsofWikipedia/status/624202342259240960 Hilbert’s hotel on wikipedia: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel types of infinity: http://www.xamuel.com/levels-of-infinity/ set theory and quantum physics: http://link.springer.com/article/10.1007/BF02213427#page-1 LHC gif: http://cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative Zermelo-Fraenkel axioms of mathematics: http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html Is math invented or discovered? http://phys.org/news/2013-09-mathematics-effective-world.html http://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/ more deep dream images: https://www.reddit.com/r/deepdream/ BOOKS: The Pea and the Sun: http://www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279 The Outer Limits of Reason: http://www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353 Why Beliefs Matter: http://www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992 Things to Make and do in the Fourth Dimension: http://www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653 Music by http://www.youtube.com/JakeChudnow and http://www.audionetwork.com
ranked in date views likes Comments ranked in country (#position)
2015-08-03 1,131,128 79,601 15,310 (Canada,#25) 
2015-08-04 1,407,054 90,000 17,275 (all,#13)  (USA,#13) 
2015-08-05 1,613,881 98,716 18,889 (all,#28)  (USA,#28)