Math

I’ve posted about this type of problem before. But now I present a simple formula to solve for all values of r. Thanks to Tony Hasler for figuring out this method! Previous video (much harder way to solve this problem) Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your favorite puzzles/suggestions
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Congratulations to Daniel Mai for winning the 2019 Raytheon MATHCOUNTS National Competition! Here’s the question that sealed his victory. Source https://www.raytheon.com/news/feature/best-when-it-counts ESPN webcast of 2019 MATHCOUNTS National Competition (I can view it now, but videos like this sometimes expire and are viewable in specific geographies–so keep that in mind if the link does not work)
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8th grade students in Turkey have to solve problems like this one. I admit I got the wrong answer! Can you figure it out? Thanks to Ata from Turkey who suggested this! Problem adapted from “Tonguc 8. Sinif Sayisal Zoru Bankasi” https://www.tongucmagaza.com/tongucmagaza/kitapdetay/155/8-sinif-sayisal-zoru-bankasi Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your
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Neil Sloane discusses peaceable queens and chess. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Learn more at the OEIS entry (loads of links): https://oeis.org/A250000 References: Ainley, Stephen. Mathematical Puzzles. London: G Bell & Sons, 1977. Yukun Yao and Doron Zeilberger, Numerical and
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Many students in the UK had difficulty with a similar problem on the GCSE exam. What’s the rectangle’s area, given the three circles are identical with radius r? Watch the video to learn how to solve this problem. Sources Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your favorite puzzles/suggestions by
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The 2017 GCSE exam featured a problem like this that confused many students. Learn how to solve it using Al-Kashi’s Theorem. Sources Emailed to me by Tom, Ben and James (GCSE 2017 exam) https://en.wikipedia.org/wiki/Jamsh%C4%ABd_al-K%C4%81sh%C4%AB Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your favorite puzzles/suggestions by email (address in video). I
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Dr James Grime discusses the mathematics of extinction. More links & stuff in full description below ↓↓↓ Extras from this interview: https://youtu.be/zomuAufWXr0 Related but different video on the math of ancestry: https://youtu.be/Fm0hOex4psA More James Grime videos: http://bit.ly/grimevideos James Grime: https://www.singingbanana.com Dice videos: http://bit.ly/Dice_Videos Thanks to the AP Archive: http://www.aparchive.com and https://youtube.com/channel/UCHTK-2W11Vh1V4uwofOfR4w Numberphile is supported by
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Dr James Grime discusses ancestry and why we ALL have royal blood. See also our new video on family extinction at: https://youtu.be/z34XhE5oRwo More links & stuff in full description below ↓↓↓ More James Grime videos: http://bit.ly/grimevideos #RoyalBaby James Grime: https://www.singingbanana.com Additional reading on this topic: http://www.stat.yale.edu/~jtc5/papers/Ancestors.pdf http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/NatureCommonAncestors-Article.pdf Numberphile is supported by the Mathematical Sciences Research
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Many students were confused about how to solve a tricky probability problem like this on the GCSE exam. Let’s go over how to solve it! Source https://math.stackexchange.com/questions/3103891/gcse-probability-question-relating-to-trees-help-please Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g Send me your favorite puzzles/suggestions by email (address in video). I get so many emails that I may
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Can you imagine a late night talk show featuring mathematical puzzles? Well back in 1982 the great Johnny Carson interviewed the great Raymond Smullyan, who shared a couple of fun logic puzzles. Can you solve them? Sources Raymond Smullyan on The Tonight Show Starring Johnny Carson Wikipedia https://en.wikipedia.org/wiki/Raymond_Smullyan Princeton obituary https://paw.princeton.edu/article/lives-raymond-m-smullyan-59 h/t FiveThirtyEight Riddler A
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A gigantic pie is shared with 100 guests, and each guest gets an increasing percentage of the remaining pie. Who gets the largest piece? Sources https://www.theguardian.com/science/2017/jun/19/did-you-solve-it-pythagorass-best-puzzles https://puzzling.stackexchange.com/questions/52787/who-get-the-biggest-piece Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon
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The legendary Elwyn Berlekamp died on April 9, 2019. In a final filming session with Numberphile, the games expert taught us how to play Amazons. More links in full description below ↓↓↓ Extras from this interview: https://youtu.be/mTl7W18UwFM Dots & Boxes with Elwyn: https://www.youtube.com/watch?v=KboGyIilP6k Elwyn’s own video on Amazons: https://youtu.be/_1NzUMWeU4c Elwyn obituary in Berkeley News: https://news.berkeley.edu/2019/04/18/elwyn-berlekamp-game-theorist-and-coding-pioneer-dies-at-78/
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Solve this equation. Then turn it upside down and solve it again. What a wonderful curiosity! The Talwalkar square (multiply by lines group theory) https://youtu.be/LmVt_KiyDC4 Sources Solve this equation for x. Then rotate it 180 and solve for x again. (Answering a challenge set by @robeastaway.) pic.twitter.com/ACSgSGpGCu — Peter Rowlett (@peterrowlett) December 17, 2018 Finding
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This is harder than it looks! Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and make the world a better place: https://www.patreon.com/mindyourdecisions If you buy from the links below I may
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Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets). More links & stuff in full description below ↓↓↓ More videos with Ben: http://bit.ly/Sparks_Playlist Ben Sparks website: https://www.bensparks.co.uk And on Twitter: https://twitter.com/sparksmaths Holly Kreiger has done a few Mandelbrot videos on Numberphile… The Mandelbrot Set: https://youtu.be/NGMRB4O922I 63 and -7/4 are special: https://youtu.be/09JslnY7W_k Pi and the
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There is now a mathematical theorem named after Sheldon. Sources Siouxland News article https://siouxlandnews.com/news/local/morningside-college-professors-math-appearing-in-the-big-bang-theory 73 is the best number – Big Bang Theory clip Proof of the Sheldon conjecture https://math.dartmouth.edu/~carlp/sheldon02132019.pdf 73 is the best number (other properties) Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math
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T-shirt and poster details below. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Featuring Neil Sloane from the OEIS: https://oeis.org And thanks to Jonathan Wild: https://www.mcgill.ca/music/jonathan-wild OEIS A250001 – Number of arrangements of n circles in the affine plane: https://oeis.org/A250001 3-Circles T-Shirt: https://teespring.com/three-circles-numberphile
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Around the world, 17-18 year old students struggled to solve this kind of question. Can you figure it out? My video on the AM-GM inequality Sources TIMSS Advanced 2015, Exhibit M2.6.2: Advanced International Benchmark – Example Item 2. http://timssandpirls.bc.edu/timss2015/international-results/advanced/download-center/ AM-GM to solve optimization problems https://www.whitman.edu/Documents/Academics/Mathematics/2016/Greff.pdf Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g
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Matt Parker has a new favourite number – again! More links & stuff in full description below ↓↓↓ Some notes from Matt on how far he has investigated: https://www.numberphile.com/cannon-ball-numbers Matt’s book “Humble Pi” via Maths Gear (signed and ships almost everywhere): http://bit.ly/Humble_Pi More Numberphile videos with Matt: http://bit.ly/Matt_Videos James Grime sphere packing: https://youtu.be/CROeIGfr3gs Lucas Numbers:
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Can you see the pattern? Apparently geniuses can figure out the answer right away. Source https://puzzling.stackexchange.com/questions/19823/mensa-iq-test-question Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and make the world a better place:
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This one stumped me! This problem is part of the AIME, a qualifying test for the US Mathematical Olympiad team. The talented students who take the AIME only average about 20 percent–it’s a hard test! Plus no calculators are allowed. Can you figure out this problem from the 1987 test? Learn the trick which results
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Fields Medallist Charlie Fefferman talks about some classic infinite series. More links & stuff in full description below ↓↓↓ Charles Fefferman at Princeton: https://www.math.princeton.edu/people/charles-fefferman Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
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It’s not so simple to solve for this simple answer. Thanks to all patrons! Special thanks this month to: Richard Ohnemus, Michael Anvari, Shrihari Puranik, Kyle. WolframAlpha http://blog.wolframalpha.com/2013/04/26/get-real-with-wolframalpha-computing-roots/ https://www.wolframalpha.com/input/?i=cuberoot(8%2B3*sqrt(21))%2Bcuberoot(8-3*sqrt(21)) https://www.wolframalpha.com/input/?i=(8%2B3*sqrt(21))%5E(1%2F3)%2B(8-3*sqrt(21))%5E(1%2F3) Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world.
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Ed Harriss discusses the plastic ratio – more amazing than the golden ratio? You decide! More links & stuff in full description below ↓↓↓ See our golden ratio videos: http://bit.ly/Golden_Ratio Previous video with Ed (Heesch Numbers): https://youtu.be/6aFcgATW9Mw Ed Harriss is online at http://maxwelldemon.com and on Twitter at https://twitter.com/gelada The Plastic Ratio Callipers were made by
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Matt Parker discusses multiplicative persistence. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Extra footage: https://youtu.be/E4mrC39sEOQ Matt’s new book is Humble Pi: http://bit.ly/Humble_Pi More Matt videos on Numberphile: http://bit.ly/Matt_Videos The Multiplicative record holders: https://oeis.org/A003001 More info: http://mathworld.wolfram.com/MultiplicativePersistence.html Hear Matt on the Numberphile podcast… http://bit.ly/Numberphile_Pod_Playlist More links & stuff in full description below
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This is a tricky SAT/GRE type problem that most people miss. Can you figure it out? Desmos animation https://www.desmos.com/calculator/kiswg6p0q7 Sources https://www.thisisinsider.com/hard-sat-math-questions-test-practice-2018-3 https://www.prepscholar.com/gre/blog/gre-geometry-review-practice/ Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and
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Marcus du Sautoy discusses Gödel’s Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy’s book as mentioned… In
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Fermat’s “Little” Theorem is great – but beware of Fermat Liars and tricky Carmichael Numbers. More links & stuff in full description below ↓↓↓ Continues at: http://youtu.be/HvMSRWTE2mI Featuring Dr James Grime – https://twitter.com/jamesgrime Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the
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Numbers like e and Pi cannot be made using normal algebra. Featuring Australia’s Numeracy Ambassador, Simon Pampena. Extra footage: http://youtu.be/dzerDfN2E7U More links & stuff in full description below ↓↓↓ Discussing transendental numbers, algebraic numbers, pi, e and other stuff. Simon’s website: http://www.numbercrunch.com.au/ Root 2: http://www.youtube.com/watch?v=5sKah3pJnHI Pi Playlist: http://www.youtube.com/playlist?list=PL4870492ACBDC2E7C NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile
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Brady Numbers T-Shirt: http://bit.ly/T-Shirt-BN Part One of Golden Ratio Trilogy More links & stuff in full description below ↓↓↓ The new “Brady Sequence” demonstrates why Fibonacci Numbers are not so special. Featuring Matt Parker. Next in the trilogy: http://youtu.be/dTWKKvlZB08 Matt’s signed book (& extra goodies): http://bit.ly/Matt_Signed Amazon (UK): http://bit.ly/Matt_4D_UK Amazon (US): http://bit.ly/Matt_4D_US Discuss this video
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Famously beautiful, the Mandelbrot Set is all about complex numbers. Featuring Dr Holly Krieger from MIT. More links & stuff in full description below ↓↓↓ The next part is on Numberphile2 at: http://youtu.be/oCkQ7WK7vuY Animation courtesy of team fresh. Check out more at: http://hd-fractals.com — Music: Alan Stewart. Support him at http://bit.ly/1sdwTHF More videos with Holly
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The Prime Number Theorem shows that primes are like weeds, popping up everywhere! Dr James Grime explains — Little bit extra cut from this video: http://youtu.be/TMRZYSQGAcw More links & stuff in full description below ↓↓↓ Our prime number video collection: http://bit.ly/primevids Follow James on Twitter at: https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile
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A million digits of Pi on one piece of paper (1.05 miles). More links & stuff in full description below ↓↓↓ More about how and why: http://youtu.be/99Welatppzk More Pi videos from Numberphile: http://bit.ly/PiPlaylist Film by Brady Haran Our thanks to HP and HSA Systems. Extra special thanks to Hugh McPartlan, Torben Dam Jensen, Jesper Hyldager
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Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be “ready” to crack. More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/O2_h3z1YgEU Prof Eisenbud’s 17-gon: https://youtu.be/87uo2TPrsl8 Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub
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This is a fun basketball problem with an unexpected result! Sources http://www.math.utah.edu/~palais/mst/frequency.pdf http://faculty.sfasu.edu/judsontw/putnam/putnam-week06-solution.pdf https://sites.math.northwestern.edu/~mlerma/problem_solving/putnam/easy_putnam_problems.pdf https://www.theringer.com/nba/2018/12/5/18126305/deandre-jordan-free-throws-mavericks https://www.basketball-reference.com/players/j/jordade01.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support on Patreon to inspire mathematical discovery and make the world a better place:
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Banks, Facebook, Twitter and Google use epic numbers – based on prime factors – to keep our Internet secrets. This is RSA public-key encryption. More links & stuff in full description below ↓↓↓ Gold Vault: https://youtu.be/CTtf5s2HFkA This video features Dr James Grime (http://singingbanana.com/). Message from James: “Thanks to Dr Chris Hughes of the University of
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Ron Graham explains the number which takes his name… More links & stuff in full description below ↓↓↓ Graham’s Number (Numberphile T-Shirt): http://bit.ly/Grahams_T-Shirt See him discuss how big it is: http://youtu.be/GuigptwlVHo Extra footage here: http://youtu.be/rGWuimr5CGQ And our original Graham’s Number video: http://youtu.be/XTeJ64KD5cg Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile
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Our Pi Playlist (more videos): http://bit.ly/PiPlaylist The State of Indiana nearly passed a law which would have made Pi equal 3.2 – strange but true. More links & stuff in full description below ↓↓↓ More Pi videos from Numberphile: http://bit.ly/W4oDN1 This video features Dr James Grime – https://twitter.com/jamesgrime The video about squaring circles: https://www.youtube.com/watch?v=CMP9a2J4Bqw A
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Simon Singh on Fermat’s Last Theorem. Simpsons book: http://amzn.to/1fKe4Yo Fermat book: http://amzn.to/1jWqMTa More links & stuff in full description below ↓↓↓ EXTRA FOOTAGE: http://youtu.be/FXbsIbRVios FERMAT IN SIMPSONS:http://youtu.be/ReOQ300AcSU Interview with Ken Ribet, who played a big role: https://youtu.be/nUN4NDVIfVI Wiles’ proof: http://bit.ly/FermatProof NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady
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Free trial at The Great Courses Plus: http://ow.ly/tKWt306Gg7a Dr James Grime discusses “e” – the famed Euler’s Number. More links & stuff in full description below ↓↓↓ A bit extra from this video: https://youtu.be/uawO3-tjP1c More James Grime videos from Numberphile: http://bit.ly/grimevideos Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:
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The Nazi’s Enigma Machine – and the mathematics behind it – was a crucial part of World War II. Flaw video at: http://www.youtube.com/watch?v=V4V2bpZlqx8 More links & stuff in full description below ↓↓↓ Brown papers on ebay: bit.ly/brownpapers Dr James Grime demonstrates the machine and discusses its many configurations. James’ “day job” is touring with the
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A number so epic it will collapse your brain into a black hole! Yet Tony Padilla and Matt Parker take the risk of discussing its magnitude. Watch with caution. More links & stuff in full description below ↓↓↓ See also our video about the Googol and Googolplex at: http://www.youtube.com/watch?v=8GEebx72-qs More about Matt and Tony at:
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We’re talking pretty big numbers here… And an interesting idea about what it’d be like traveling in a Googolplex-sized Universe! More links & stuff in full description below ↓↓↓ With Antonio (Tony) Padilla and Ria Symonds from the University of Nottingham. About the brown paper: http://periodicvideos.blogspot.com/2012/02/brown-paper-question.html NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:
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Why squaring the circle – the old-fashioned way – was found to be impossible? Numblr: http://numberphile.tumblr.com/ More links & stuff in full description below ↓↓↓ This video featuring Dr James Grime: https://twitter.com/jamesgrime The paper from this video on ebay – http://bit.ly/brownpapers NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by
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