The Banach–Tarski Paradox
43,521,420
Published 2015-07-31
Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infin…
Chocolate illusion video: • Video
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Vi Hart on types of infinity: • How many kinds of infinity are there?
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_parado…
Banach-Tarski proofs:
math.uchicago.edu/~may/REU2014/REUPapers/Robinson.…
www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
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?pid…
skepticsplay.blogspot.co.uk/2010/05/doubling-spher…
austinrochford.com/posts/2014-05-14-banach-tarski-…
www.math.cornell.edu/~mec/Summer2009/Whieldon/Math…
rachellevanger.com/index_files/BT%20Animated%20Pre…
quibb.blogspot.co.uk/2013_03_01_archive.html
blog.computationalcomplexity.org/2011/04/what-did-…
geopolicraticus.wordpress.com/tag/banach-tarski-pa…
dgleahy.com/p47.html
www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml
Cayley graph animated gif: twitter.com/GIFsofWikipedia/status/624202342259240…
Hilbert’s hotel on wikipedia: en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_G…
types of infinity: www.xamuel.com/levels-of-infinity/
set theory and quantum physics: link.springer.com/article/10.1007/BF02213427#page-…
LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-…
Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
Is math invented or discovered?
phys.org/news/2013-09-mathematics-effective-world.…
www.scientificamerican.com/article/is-the-universe…
more deep dream images: www.reddit.com/r/deepdream/
BOOKS:
The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp…
The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathema…
Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Scie…
Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathem…
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