The Banach–Tarski Paradox

Want more brain food? Want your house to become a museum? Now you're thinking: http://www.curiositybox.com

Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."

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Kevin’s Field Day video: https://www.youtube.com/watch?v=1zARMZ08ums

Field Day: https://www.youtube.com/channe....l/UCRPktNf5vnBR1J4e7

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/2....014/07/22/explanatio

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%93Tarsk

Banach-Tarski proofs:

http://math.uchicago.edu/~may/....REU2014/REUPapers/Ro
https://www.math.hmc.edu/~su/p....apers.dir/banachtars
http://people.math.umass.edu/~....weston/oldpapers/ban

Banach-Tarski explinations online:

http://www.irregularwebcomic.net/2339.html
http://www.kuro5hin.org/commen....ts/2003/5/23/134430/
http://skepticsplay.blogspot.c....o.uk/2010/05/doublin
http://austinrochford.com/post....s/2014-05-14-banach-
http://www.math.cornell.edu/~m....ec/Summer2009/Whield
http://rachellevanger.com/inde....x_files/BT%20Animate
http://quibb.blogspot.co.uk/20....13_03_01_archive.htm
http://blog.computationalcompl....exity.org/2011/04/wh
https://geopolicraticus.wordpr....ess.com/tag/banach-t
http://dgleahy.com/p47.html
https://www.math.hmc.edu/funfa....cts/ffiles/30001.1-3

Cayley graph animated gif: https://twitter.com/GIFsofWiki....pedia/status/6242023

Hilbert’s hotel on wikipedia: https://en.wikipedia.org/wiki/....Hilbert%27s_paradox_

types of infinity: http://www.xamuel.com/levels-of-infinity/

set theory and quantum physics: http://link.springer.com/artic....le/10.1007/BF0221342

LHC gif: http://cms.web.cern.ch/news/lh....c-data-be-made-publi

Zermelo-Fraenkel axioms of mathematics: http://mathworld.wolfram.com/Z....ermelo-FraenkelAxiom

Is math invented or discovered?

http://phys.org/news/2013-09-m....athematics-effective
http://www.scientificamerican.....com/article/is-the-u

more deep dream images: https://www.reddit.com/r/deepdream/

BOOKS:

The Pea and the Sun: http://www.amazon.com/The-Pea-....Sun-Mathematical-Par
The Outer Limits of Reason: http://www.amazon.com/Outer-Li....mits-Reason-Science-
Why Beliefs Matter: http://www.amazon.com/Why-Beli....efs-Matter-Reflectio
Things to Make and do in the Fourth Dimension: http://www.amazon.com/Things-M....ake-Fourth-Dimension

Music by http://www.youtube.com/JakeChudnow and
http://www.audionetwork.com