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Published on 01 Aug 2015 | about 1 year ago

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

twitter: www.twitter.com/tweetsauce
Instagram: www.instagram.com/electricpants

Kevin’s Field Day video: www.youtube.com/watch

Field Day: www.youtube.com/channel/UCRPktNf5vnBR1J4e7t1RUVg

Deep dream animation by instagram.com/NaderMakki/

If you like it, you'll love this video also by Nader: www.youtube.com/watch

Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/

Chocolate illusion video: www.youtube.com/watch

related Numberphile videos:

sizes of infinity (includes diagonal argument): www.youtube.com/watch
infinity paradoxes: www.youtube.com/watch

Vi Hart on types of infinity: www.youtube.com/watch
Countable & uncountable definitions:

mathinsight.org/definition/uncountable
en.wikipedia.org/wiki/Countable_set
en.wikipedia.org/wiki/Uncountable_set

Banach-Tarski on wikipedia: 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:

www.irregularwebcomic.net/2339.html
www.kuro5hin.org/comments/2003/5/23/134430/275
skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html
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
rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf
quibb.blogspot.co.uk/2013_03_01_archive.html
blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html
geopolicraticus.wordpress.com/tag/banach-tarski-paradox/
dgleahy.com/p47.html
www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml

Cayley graph animated gif: twitter.com/GIFsofWikipedia/status/624202342259240960

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

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

set theory and quantum physics: link.springer.com/article/10.1007/BF02213427

LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative

Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

Is math invented or discovered?

phys.org/news/2013-09-mathematics-effective-world.html
www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/

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

BOOKS:

The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279
The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353
Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992
Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653

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

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