singingbanana
https://youtube.com/channel/UCMpizQXRt817D0qpBQZ2TlA
Mathematician, juggler and comedy nerd - but not necessarily in that order.
Please keep sending your messages. I do read them all, even if I don't always have time to reply :(
- JimCHANGE_ITPodsync generator (support us at https://github.com/mxpv/podsync)en-usMon, 23 Nov 2020 23:36:25 +0000Sun, 26 Mar 2006 22:32:01 +0000https://yt3.ggpht.com/ytc/AAUvwnheoGNC4hKyjfD8I4C8uFjSbaQNPVcpazzRuFsy=s800-c-k-c0x00ffffff-no-rjsingingbanana
https://youtube.com/channel/UCMpizQXRt817D0qpBQZ2TlA
singingbananasingingbanananohttp://yt2podcast.com:8080/TV-SingingBanana/kVs9nFhcX_8.mp4A MegaFavNumbers Thank You!
https://youtube.com/watch?v=kVs9nFhcX_8
See the full #MegaFavNumbers playlist here https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAoTue, 08 Sep 2020 15:33:00 +0000singingbananaA MegaFavNumbers Thank You!1:49no0http://yt2podcast.com:8080/TV-SingingBanana/R2eQVqdUQLI.mp4MegaFavNumbers - The Even Amicable Numbers Conjecture
https://youtube.com/watch?v=R2eQVqdUQLI
This video is part of the MegaFavNumbers project. Maths YouTubers have come together to make videos about their favourite numbers bigger than one million, which we are calling #MegaFavNumbers.
We want *you*, the viewers, to join in! Make your own video about your favourite mega-number. You can think of a cool big number, or think of a cool topic first and hang a mega-number on it.
Upload your videos to YouTube with the hashtag #MegaFavNumbers and with MegaFavNumbers in the title, and your video will be added to the megafavnumbers playlist.
Submit your videos anytime before Wednesday 2nd September to be added to the MegaFavNumbers playlist!
MegaFavNumbers Playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo
Amicable Numbers on Wikipedia:
https://en.wikipedia.org/wiki/Amicable_numbers
Here is a list of amicable numbers:
http://www.vaxasoftware.com/doc_eduen/mat/numamigos_eng.pdf
A list of sums of amicable numbers
https://oeis.org/A180164
Remember, a test for divisibility by 9 is to add all the digits of the number together, and to do the same with the result, until you get a single digit. If the end result is 9 then the original number was a multiple of 9.
Here is a list of even amicable numbers whose sum is not divisible by 9 https://oeis.org/A291550
And here are those complicated mathematical conditions
https://www.ams.org/journals/mcom/1969-23-107/S0025-5718-1969-0248074-6/S0025-5718-1969-0248074-6.pdfThu, 13 Aug 2020 16:36:09 +0000singingbananaMegaFavNumbers - The Even Amicable Numbers Conjecture5:54no1http://yt2podcast.com:8080/TV-SingingBanana/y_LKxvjuiSg.mp4I'm making videos on MathsWorldUK and this is me telling you about it
https://youtube.com/watch?v=y_LKxvjuiSg
See the videos at https://www.youtube.com/user/MathsWorldUK
At the moment, we've made 12 and they will be released over the next few weeks.
Here's more about MathsWorldUK http://mathsworlduk.com/Fri, 12 Jun 2020 13:09:47 +0000singingbananaI'm making videos on MathsWorldUK and this is me telling you about it1:44no2http://yt2podcast.com:8080/TV-SingingBanana/rwtDBhD6Mq0.mp4Bayes Billiards with Tom Crawford
https://youtube.com/watch?v=rwtDBhD6Mq0
Bayes' Theorem allows us to assign a probability to an unknown fact.
Thomas Bayes himself described an experiment with a billiard table, which is brilliantly explained by Hannah Fry and Matt Parker here https://www.youtube.com/watch?v=7GgLSnQ48os
Brian Cox and David Spiegelhalter did a 1-dimensional version similar to our experiment here https://www.youtube.com/watch?v=-e8wOcaascM
After we filmed this video, 3blue1brown released his own Bayesian video https://www.youtube.com/watch?v=HZGCoVF3YvM
For more of Tom Crawford see his channel https://www.youtube.com/tomrocksmaths
Our experiment failed pretty badly really. For some behind-the-scenes information, this was our third attempt at the experiment, the first two were a little slow. The previous attempts were a lot more accurate. Oh well.
Why did we fail? Maybe because the balls were colliding they were not independent. Maybe Tom wasn't random enough. In which case, our assumption that each position is equally likely could be updated.
For more information on this experiment see https://www.nature.com/articles/nbt0904-1177
The main point, I believe, is that for limited data, the Bayesian approach (using the average estimate) is more accurate.
Viewer, Penny Lane, has run a simulation of this experiment, which did show that Bayesian was slightly more accurate than Frequentist (so this real-life attempt was probably a toss up for who did best):
"Here's the output of my script:
simulated 14 balls 10000000 times
the Bayesian approach won over the Frequentist one 50.44934% of the times
6.65762% of the simulations were ties, so 42.89304% were Frequentist wins
the mean deviation from the real value for the Bayesian approach was: 0.0800043179873167
the mean deviation from the real value for the Frequentist approach was: 0.08422584547321381"
See the comment here http://youtube.com/watch?v=rwtDBhD6Mq0&lc=UgzUC4MfbeHpIPQsBSR4AaABAg
And code here https://pastebin.com/yyCjtnEu
Another comment I liked talked about what would happen if all the balls had been to the right. In that case the frequentist approach would put the position on the extreme left, p=0. While the Bayesian approach would put the position at p = 1/16 = 0.0625, so a little way from the extreme. And that sounds sensible.
People who read the description are the best people. If you have read this, I probably need cheering up after the failure of this experiment, so tell me a joke in the comments. Thanks.Thu, 23 Jan 2020 19:13:29 +0000singingbananaBayes Billiards with Tom Crawford15:00no3http://yt2podcast.com:8080/TV-SingingBanana/b52sCDFlRuo.mp4Help us make a maths discovery centre in the UK
https://youtube.com/watch?v=b52sCDFlRuo
I'm talking to Dr Katie Chicot CEO of Maths World UK ( http://mathsworlduk.com/ ) - an organisation dedicated to creating a maths discovery centre in the UK.
Although maths discovery centres exist in other countries we have nothing like it in the UK, that is what Maths World UK want to change.
We ask for your ideas for what you would like to see in a maths discovery centre and show off a few puzzles and pretty mathematical objects.
At the moment Maths World UK has funding to creating a travelling exhibition that will be visiting science centres. Maths World UK are currently looking for funding to create a permanent home.
I really want to see a maths discovery centre in UK, but at the moment we have no permanent home. So if you know any friendly millionaires, let them know. (That's not a joke, that's what we need).Thu, 25 Apr 2019 16:23:07 +0000singingbananaHelp us make a maths discovery centre in the UK8:27no4http://yt2podcast.com:8080/TV-SingingBanana/_PyPOXXPIJQ.mp4A Pythagorean Theorem for Pentagons + Einstein's Proof
https://youtube.com/watch?v=_PyPOXXPIJQ
Pythagoras's Theorem is the most famous theorem in mathematics, commonly stated as "the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides."
However, Pythagoras's Theorem is not just for squares. In fact it works for any shape.
The proof relies on the fact that scaling a shape by c will scale the area by c^2. Then, if Pythagoras's Theorem is true then the area of the shape on the hypotenuse will be equal to the total areas of the similar shapes on the other two sides.
More succinctly, if Pythagoras's Theorem is true then the areas will be equal.
But we can prove Pythagoras's Theorem itself by running that argument in reverse - if the shapes have equal area then Pythagoras's Theorem is true.
This is an argument an 11 year old Albert Einstein used to prove Pythagoras's Theorem for himself.
There are a couple of things I wished I said clearer in the Einstein proof:
The Einstein proof divides the triangle so we have three right-angled triangles (but I think that was clear from the picture)
Secondly, the three triangles are scaled versions of a triangle with a hypotenuse of length 1 and area X, which then have areas scaled by a^2, b^2 and c^2. (I just said "some triangle").
This topic has been done before by a couple of the big maths YouTube channels, which I didn't know at the time (or forgot).
Numberphile did it in 2014 https://www.youtube.com/watch?v=ItiFO5y36kw
And Mathologer did it in 2018 https://www.youtube.com/watch?v=p-0SOWbzUYI
A little historical note, Pythagoras's Theorem appears twice in Euclid's Elements, the famous squares version appears in Book 1.47, and in Book 6.31 it is there again, this time for any shape.Tue, 02 Apr 2019 11:32:01 +0000singingbananaA Pythagorean Theorem for Pentagons + Einstein's Proof6:53no5http://yt2podcast.com:8080/TV-SingingBanana/MTf_WcKUg2Y.mp4Fermat's Last Theorem for rational and irrational exponents
https://youtube.com/watch?v=MTf_WcKUg2Y
Fermat's Last Theorem states the equation x^n + y^n = z^n has no integer solutions for positive integer exponents greater than 2. However, Fermat's Last Theorem says nothing about exponents that are not positive integers.
Note: x, y and z are meant to be positive integers, which I should have said in the video. Whoops.
This video introduces some results for rational and irrational exponents.
For rational exponents, k/m, k must be equal to 1 or 2.
If we allow complex roots, then we have strange solutions with x=y=z and m divisible by 6.
For irrational exponents no general results exist but we know there are infinitely many integer solutions, in this video I give a couple of examples.
Many of the examples in this video, as well as the proof for rational exponents, were taken from this paper by Frank Morgan (2010) https://www.maa.org/sites/default/files/pdf/cmj_ftp/CMJ/May%202010/3%20Articles/1%20Morgan/Morgan9_5_09.pdf
Here is another description of the same proof, with a bit more detail https://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/1992d/art.pdf
Another proof for rational exponents is here, as well as the result with complex roots, by Bennett, Glass, Székely (2004)
https://digitalcommons.lmu.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1103&context=math_fac
The result for rationals seems to have been first proven by R. Oblath. Quelques proprietes arithmetiques des radicaux (Hungarian). In Comptes Rendus du Premier Congres des Mathematiciens Hongrois, 27 Aout–2 Septembre 1950, pages 445–450. Akad´emiai Kiado,
Budapest, 1952.Wed, 27 Feb 2019 10:10:31 +0000singingbananaFermat's Last Theorem for rational and irrational exponents7:18no6http://yt2podcast.com:8080/TV-SingingBanana/AsYfbmp0To0.mp4The Elo Rating System for Chess and Beyond
https://youtube.com/watch?v=AsYfbmp0To0
The Elo Rating system is a method to rate players in chess and other competitive games. A new player starts with a rating of 1000. This rating will go up if they win games, and go down if they lose games. Over time a player's rating becomes a true reflection of their ability - relative to the population.
My video was mostly based on A Comprehensive Guide to Chess Ratings by Prof Mark E Glickman http://www.glicko.net/research/acjpaper.pdf
Below are some of the things I wanted to talk about, but cut so the video wasn't too long!
Some explanations of the Elo rating system say it is based on the normal distribution, which is not quite true. Elo's original idea did model each player's ability as a normal distribution. The difference between the two players strengths would then also be a normal distribution. However, the formula for a normal distribution is a bit messy so today it is preferred to model each player using an extreme value distribution. The difference between the two players strengths is then a logistic distribution. This has the property that if a player has a rating 400 points more than another player they are 10 times more likely to win, this makes the formula nicer to use. Practically, the difference between a logistic distribution and the normal distribution is small.
Logistic distribution on Wikipedia https://en.wikipedia.org/wiki/Logistic_distribution?wprov=sfla1
We replace e with base 10, s=400, mu=R_A - R_B and x=0 in the cdf.
For the update formula I say that your rating can increase or decrease by a maximum of 32 points, and I said there was no special reason for that. This value is called the K-factor, and the higher the K-factor the more weight you give to the players tournament performance (and so less weight to their pre-tournament performance). For high level chess tournaments they use a K-factor of 16 as it is believed their pre-tournament rating is about right, so their rating will not fluctuate as much. Some tournaments use different K-factors.
In the original Elo system, draws are not included, instead they are considered to be equivalent to half a win and half a loss. The paper by Mark Glickman above contains a formula that includes draws. Similarly the paper contains a formula that includes the advantage to white.
Another criticism of Elo is the reliability of the rating. The rating of an infrequent player is a less reliable measure of that player's strength, so to address this problem Mark Glickman devised Glicko and Glicko2. See descriptions of these methods at http://www.glicko.net/glicko.html
On the plus side, the Elo system was leagues ahead of what it replaced, known as the Harkness system. I originally intended to explain the Harkness system as well, so here are the paragraphs I cut:
"In the Harkness system an average was taken of everyone's rating, then at the end of the tournment if the percentage of games you won was 50% then your new rating was the average rating.
If you did better or worse than 50% then 10 points was added or subtracted to the average rating for every percentage point above or below 50.
This system was not the best and could produce some strange results. For example, it was possible for a player to lose every game and still gain points."
This video was suggested by Outray Chess. The maths is a bit harder, but I liked the idea so I made a in-front-of-a-wall video.Fri, 15 Feb 2019 17:52:30 +0000singingbananaThe Elo Rating System for Chess and Beyond7:09no7http://yt2podcast.com:8080/TV-SingingBanana/ZwJlOJuhbOw.mp4The Infinite Game of Chess (with Outray Chess)
https://youtube.com/watch?v=ZwJlOJuhbOw
An infinite game of chess with the Thue-Morse sequence.
To avoid an infinite game of chess there was a rule that declared that a game would end if any sequence of moves were repeated three times in a row.
However Dutch mathematician Max Euwe showed that the Thue-Morse sequence can define an infinite game since it contains no finite sequence that is repeated three times in a row.
The Thue-Morse sequence is made from building blocks of 0110 and 1001, so we know it cannot contain short repetitions like 000, 111, 010101 or 101010.
Double digits in the Thue-Morse sequence always appear in the odd positions (starting from position zero), which is not possible if a sequence of odd length is repeated. So the Thue-Morse sequence does not contain any finite sequence of odd length repeated three times in a row.
If we remove every second digit of the Thue-Morse sequence we will still have the Thue-Morse sequence. If you apply this to any finite sequence of even length that is repeated three times in a row, you will get a sequence half the length that also repeats three times in a row. Repeat this process until you reach a sequence of odd length repeated three times or a short sequence repeated three times. Since we know this shorter repeated sequence is not contained in the Thue-Morse sequence it implies the original repeated sequence is not contained in the Thue-Morse sequence.
The argument above is enough to show that the Thue-Morse sequence does not contain a finite sequence of any length repeated three times in a row.
You can read a little more detail here https://homepages-fb.thm.de/boergens/english/problems/problem059englloe.htm
Thanks to Outray Chess for making this video.
Outray Chess https://www.youtube.com/channel/UCVfSsCg38hOzrezIFvMz9oA/featured
Host: Rune Friborg
Camera: Mathis Eskjær
Editing: Mathis Eskjær and Rune Friborg
Finally, here is our video about Hugh Alexander, as promised https://youtu.be/im75EwDXEzgFri, 08 Feb 2019 11:05:51 +0000singingbananaThe Infinite Game of Chess (with Outray Chess)8:47no8http://yt2podcast.com:8080/TV-SingingBanana/cMxbSsRntv4.mp4Alan Turing's lost radio broadcast rerecorded
https://youtube.com/watch?v=cMxbSsRntv4
On the 15th of May 1951 the BBC broadcasted a short lecture on the radio by the mathematician Alan Turing.
His lecture was titled “Can Digital Computers Think?” and was part of a series of lectures which featured other leading figures in computing at the time.
Unfortunately, these recording no longer exist, along with all other recordings of Alan Turing. The following is a rerecording of Alan Turing’s lost broadcast from his original script.
See Turing's script at the Turing Digital Archive from King's College, Cambridge: http://www.turingarchive.org/browse.php/B/5
For more information on the radio series see: http://oro.open.ac.uk/5609/1/01299654.pdf
Photo: Alan Turing (right) at the console of Mark II computer, c. 1951, at the University of Manchester.Sun, 24 Dec 2017 20:52:36 +0000singingbananaAlan Turing's lost radio broadcast rerecorded15:33no9http://yt2podcast.com:8080/TV-SingingBanana/AYOB-6wyK_I.mp4Wythoff's Game (Get Home)
https://youtube.com/watch?v=AYOB-6wyK_I
Wythoff's Game is played on a chessboard. Two players take it in turns to move a piece. That piece can move any number of square to the left, and number of squares down, or any number of squares on a down-left diagonal. The winner is the player who moves the piece to the bottom-left square. What are the losing squares?
See my first video with Katie Steckles here https://youtu.be/pzlpi7lJi4k
--
If we call the bottom-left square (0,0) then the losing squares are (1,2), (3,5), (4,7) and their reflections that swap the coordinates.
The losing squares can be generated one at a time using the following two conditions: First, for the nth losing square, the difference between its coordinates is n. And second, each positive integer appears once and only once as either the x or y coordinate of a losing square.
These two conditions have the effect of putting all losing squares on different rows, columns and diagonals.
In 1907, Willem Wythoff proved that the nth losing square has coordinates (n*phi, n*phi^2) where phi is the golden ratio (1.618), and the two coordinates are rounded down to the previous integer. He showed that the golden ratio is the only number that will work in this way, giving the desired two properties of losing squares.
Play an interactive version of the nim version of Wythoff's Game (called Last Biscuit here) on nrich: https://nrich.maths.org/1186
Wythoff's Game on Wikipedia:
https://en.wikipedia.org/wiki/Wythoff%27s_game
Wythoff's Game on Mathworld: http://mathworld.wolfram.com/WythoffsGame.html
Wythoff's Proof: https://archive.org/stream/nieuwarchiefvoo03genogoog#page/n219/mode/2up
An excellent series of blog posts by Zachary Abel, read in reverse order (Thanks to Daniel Kelsall for this link) http://blog.zacharyabel.com/tag/wythoffs-game/
Willem Wythoff: https://en.wikipedia.org/wiki/Willem_Abraham_Wythoff
Rufus Isaacs: https://en.wikipedia.org/wiki/Rufus_Isaacs_(game_theorist)Fri, 18 Aug 2017 19:39:51 +0000singingbananaWythoff's Game (Get Home)4:52no10http://yt2podcast.com:8080/TV-SingingBanana/pzlpi7lJi4k.mp4Game: Get Home
https://youtube.com/watch?v=pzlpi7lJi4k
A game with a winning strategy.
Place a piece a grid (like a chessboard). Two players take it in turns to move the piece. You can move any number of squares to the left; and number of squares down; and any number of squares left-down (SW diagonal). No other moves are allowed. The winner is the player who moves the piece to the bottom-left square.
What is the winning strategy? Is there a winning strategy for every square? Does it matter if you go first or second?
Katie Steckles https://www.youtube.com/user/st3cksMon, 14 Aug 2017 17:42:10 +0000singingbananaGame: Get Home3:57no11http://yt2podcast.com:8080/TV-SingingBanana/wA5HO-VIv5M.mp4Twin Primes Problem
https://youtube.com/watch?v=wA5HO-VIv5M
Prove that when you multiply a pair of twin primes you get a number that has remainder 8 after division by 9. With one exception.
I'm already getting some good solutions. It's interesting to see people do it in slightly different ways.
I'll kill some space here just in case people can see the beginning of the description if it gets reposted.
OK, I think the most succinct answers go along these lines:
Twin primes must be of the form 3n-1 and 3n+1. Multiplying these two primes gives us 9n^2 - 1 = 9(n^2 - 1) + 8. So we have a remainder of 8 after division by 9. The exception is 3 and 5.
I've summarised answers there, but Alienturnedhuman was the first commenter who said something like that.
Some people used the same argument using 6n-1 and 6n+1. It is true that all primes larger than 3 are of this form. That works as well, but it's not quite as neat as above.
Some people used modular arithmetic. I can't assume all viewers know modular arithmetic, but one argument is:
All primes are 1, 2, 4, 5, 7, 8 mod 9 The possible pairs are
2x4 = 8 mod 9
5x7 = 35 = 8 mod 9
8x1 = 8 mod 9.
That's actually how I did it when given the problem. It's not the neatest solution.Sun, 04 Jun 2017 12:19:26 +0000singingbananaTwin Primes Problem1:05no12http://yt2podcast.com:8080/TV-SingingBanana/aeyhnrZvQBE.mp4Cambridge has a new mathsy train station
https://youtube.com/watch?v=aeyhnrZvQBE
Cambridge North is the new train station in Cambridge which features a mathematical design. The architects said the design was "derived from John Conway's Game of Life". Except it's not the Game of Life. It is Stephen Wolfram's Rule 135.
Find out more about Rule 135 (or Rule 30, which is the same thing with the colours swapped) https://en.wikipedia.org/wiki/Rule_30
Here's is Stephen Wolfram's reaction on his blog http://blog.stephenwolfram.com/2017/06/oh-my-gosh-its-covered-in-rule-30s/
Thanks to SRD who spotted this on twitter https://twitter.com/Quendus/status/866707269299339264
Here is the architect's website about Cambridge North http://www.atkinsglobal.com/en-gb/projects/cambridge-north-station
The architects respond in the comments under this article http://aperiodical.com/2017/05/right-answer-for-the-wrong-reason-cellular-automaton-on-the-new-cambridge-north-station/
"Let me assure you it is the correct answer. We turned the pattern through 45 degrees, distorted the pixels to a slightly elongated diamond and played about with the panel dimensions to ensure the maximum gathering of openings around eye level for the passengers using the station. What we liked most about rule 30 was it was as close as we could find to a “random” non repeating pattern.
Quintin Doyle, Senior Architectural Designer, Atkins."
The irony is, Stephen Wolfram went to Oxford.
------------------------
Corrections:
I misspoke three times. Silly mistakes, but more than usual, and quite close together. I miss YouTube annotations, that would have sorted it out.
"John Conway was" - That was definitely a slip of the tongue. My mind was picturing 1970 so was speaking in past tense.
"Take that Oxford" - I thought that was quite funny. Apparently Oxford has two stations too. So that spoilt the joke.
"Stephen Wolfram is American" - He was British, and is now an American citizen. People didn't like me calling him American.
And a personal request from me. When you comment you are talking directly to me. Please be respectful. I make videos in my spare time and for fun. I'm just a guy.Fri, 26 May 2017 10:02:08 +0000singingbananaCambridge has a new mathsy train station2:59no13http://yt2podcast.com:8080/TV-SingingBanana/ULN43aYDJDY.mp4A visit from Rafael Procopio (Matemática Rio)
https://youtube.com/watch?v=ULN43aYDJDY
I was visited by Rafael Procopio from Matemática Rio.
YouTube channel: https://www.youtube.com/user/matematicario/featured
Our video about the Walkie-Talkie building: https://www.youtube.com/watch?v=2of5DuORwj8
An interview we did: https://www.youtube.com/watch?v=oPoJMJ2HGsg
Rafael on twitter https://twitter.com/MatematicaRioThu, 29 Sep 2016 11:20:35 +0000singingbananaA visit from Rafael Procopio (Matemática Rio)1:27no14http://yt2podcast.com:8080/TV-SingingBanana/UNiFELOL42w.mp4Origami Soma Cube
https://youtube.com/watch?v=UNiFELOL42w
The soma cube is a famous puzzle among mathematicians. Seven tetris-like pieces fit together to make a 3x3 cube. I made one from post-it notes.
My instructions for the sonobe units: https://www.youtube.com/watch?v=uF72h-7xe0g
A blog with instructions if you don't like mine (sob) https://luckpaperscissors.wordpress.com/2013/05/09/make-a-soma-cube-out-of-sonobe-modules/
My friend Alison Kiddle https://twitter.com/ajk_44Fri, 23 Sep 2016 12:57:02 +0000singingbananaOrigami Soma Cube2:22no15http://yt2podcast.com:8080/TV-SingingBanana/CWhcUea5GNc.mp4Sum of Fibonacci Numbers Trick
https://youtube.com/watch?v=CWhcUea5GNc
A little trick to sum Fibonacci numbers. Try it out.Sun, 18 Sep 2016 18:32:55 +0000singingbananaSum of Fibonacci Numbers Trick6:08no16http://yt2podcast.com:8080/TV-SingingBanana/gSMeawFz0Sw.mp4The International Maths Salute with Dr James Tanton
https://youtube.com/watch?v=gSMeawFz0Sw
I caught James at the MATRIX conference in Leeds in September 2016. I'm a fan of his work so this was cool. We grabbed a moment to make a super quick video.
Go see James' videos on his YouTube channel https://www.youtube.com/user/DrJamesTanton
Some more videos with James via the MAA https://www.youtube.com/playlist?list=PLevtNOOa6SZXVJvtROAFCC0oYt0ySTSo4
James' Twitter: https://twitter.com/jamestanton
And websites: http://gdaymath.com/ http://www.jamestanton.com/Thu, 08 Sep 2016 12:10:13 +0000singingbananaThe International Maths Salute with Dr James Tanton1:31no17http://yt2podcast.com:8080/TV-SingingBanana/2HHhGl1vMqk.mp4Ten years on YouTube
https://youtube.com/watch?v=2HHhGl1vMqk
Jim Bob scores a hat trick https://youtu.be/HkcoKbr5NjQSun, 04 Sep 2016 09:06:14 +0000singingbananaTen years on YouTube0:47no18http://yt2podcast.com:8080/TV-SingingBanana/OiGYgP04MD8.mp4Ramanujan Review
https://youtube.com/watch?v=OiGYgP04MD8
A sort of review of The Man Who Knew Infinity. And a *review* of other videos that came out this week.
standupmaths: Ramanujan, 1729, Fermat's Last Theorem https://www.youtube.com/watch?v=_o0cIpLQApk
Mathologer: Ramanujan. Making sense of -1/12 https://www.youtube.com/watch?v=jcKRGpMiVTw
singingbanana: The Riemann Hypothesis https://www.youtube.com/watch?v=rGo2hsoJSbo
singingbanana: Ramanujan Summation https://www.youtube.com/watch?v=8hgeIDY7We4
Numberphile: Partitions https://www.youtube.com/watch?v=NjCIq58rZ8I
Other videos I found too late to recommend in the video:
Tipping Point Math: The Man Who Knew Infinity https://www.youtube.com/watch?v=P0idBBhGNgU
MindYourDecisions: Ramanujan's Radical Brainteaser https://www.youtube.com/watch?v=r5BGIi84arYMon, 02 May 2016 16:19:46 +0000singingbananaRamanujan Review1:57no19