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The Banach–Tarski Paradox

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Vsauce

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=1zARM...

Field Day: https://www.youtube.com/channel/UCRPk...

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_...

Chocolate illusion: http://mathandmultimedia.com/2014/07/...

Chocolate illusion video: https://www.youtube.com/watch?v=dmBsP...

related Numberphile videos:

sizes of infinity (includes diagonal argument): https://www.youtube.com/watch?v=elvOZ...
infinity paradoxes: https://www.youtube.com/watch?v=dDl7g...

Vi Hart on types of infinity: https://www.youtube.com/watch?v=23I5G...
Countable & uncountable definitions:

http://mathinsight.org/definition/unc...
https://en.wikipedia.org/wiki/Countab...
https://en.wikipedia.org/wiki/Uncount...

Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%...

Banach-Tarski proofs:

http://math.uchicago.edu/~may/REU2014...
https://www.math.hmc.edu/~su/papers.d...
http://people.math.umass.edu/~weston/...

Banach-Tarski explinations online:

http://www.irregularwebcomic.net/2339...
http://www.kuro5hin.org/comments/2003...
http://skepticsplay.blogspot.co.uk/20...
http://austinrochford.com/posts/2014-...
http://www.math.cornell.edu/~mec/Summ...
http://rachellevanger.com/index_files...
http://quibb.blogspot.co.uk/2013_03_0...
http://blog.computationalcomplexity.o...
https://geopolicraticus.wordpress.com...
http://dgleahy.com/p47.html
https://www.math.hmc.edu/funfacts/ffi...

Cayley graph animated gif: https://twitter.com/GIFsofWikipedia/s...

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

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

set theory and quantum physics: http://link.springer.com/article/10.1...

LHC gif: http://cms.web.cern.ch/news/lhc-data-...

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

Is math invented or discovered?

http://phys.org/news/2013-09-mathemat...
http://www.scientificamerican.com/art...

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

BOOKS:

The Pea and the Sun: http://www.amazon.com/The-Pea-Sun-Mat...
The Outer Limits of Reason: http://www.amazon.com/Outer-Limits-Re...
Why Beliefs Matter: http://www.amazon.com/Why-Beliefs-Mat...
Things to Make and do in the Fourth Dimension: http://www.amazon.com/Things-Make-Fou...

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

posted by rekjastv8