singingbanana

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=_o0cIpLQ...

The third video in a series about Ramanujan.This one is about Ramanujan Summation.

Here's the wikipedia page for further reading: https://en.wikipedia.org/wiki/Ramanujan_summation

Euler-Maclaurin...

The second video in a series about Ramanujan. Continuing the biography and a look at another of Ramanujan's formulas. This one involves Ramanujan's pi formula.

The first video in a series about Ramanujan. A bit of biography then a look at one of Ramanujan's formulas. This one involves infinite nested radicals.

Here's a more formal look at Ramanujan's nes...

Here is my solution video: https://youtu.be/pTpBcxIg-9A

Here is the solution and results from the problem by Alex Bellos https://www.theguardian.com/science/2016/mar/28/did-you-s......

Jack is looking Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?
A) Yes B) No C) Cannot be determined

Here is the soluti...

Jack is looking Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?
A) Yes B) No C) Cannot be determined

Unfortunately the ...

Solution to the self descriptive number puzzle https://www.youtube.com/watch?v=K6Qc4oK_HqY

Here is the original version of the proof presented in the video http://singingbanana.com/self%20describi...

I have a ten digit number. The first digit tells me how many zeros are in the number. The second digit tells me how many ones are in the number. The third digit tells me how many twos are in the nu...

2016 is the beginning of a new century - if you count in twelves. If you do that then the year 2016 becomes the year 1200.

Counting in twelves is known as the dozenal system, and a "century" in d...

Cheryl's Birthday problem was a question in a recent Singapore Maths Olympiad. Here is the problem:


You have Albert, Bernard and Cheryl. Cheryl says "my birthday is one of these ten dates"

May 1...

For more of my thoughts read The Imitation Game FAQs here http://aperiodical.com/2014/11/an-alan-turing-expert-answ...

Many people have heard of Enigma before, the code machine used by Nazi Germany to send secret coded messages. Yet, some very clever code breakers were able to break that code and read those message...

Turn a cubic curve (with no x^2 term) into a calculator for sums, multiplications and square-roots.

Simply draw a line across the curve so that it intersects at three points, a, b and c. We may no...

James Grime's youtube channel is:
http://www.youtube.com/user/singingbanana

You can play 2048 here:
http://gabrielecirulli.github.io/2048/

You can watch it being played by AI here:
http://ov3y.gi...

An extra bit from our 2048 video on Steve Mould's channel.

Full video here: 2048 strategy and maths http://youtu.be/OO4tA5i7X9g

Play 2048 here http://gabrielecirulli.github.io/2048/

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Problem video http://www.youtube.com/watch?v=YMkziQhJkmM

Imagine the line from 0 to 1. Write a sequence of points such that the first two points occupy different halves, the first three occupy dif...

Imagine the line from 0 to 1. Write a sequence of points such that the first two points occupy different halves, the first three occupy different thirds, the first four occupy different fourths, an...

A new mathematical proof was in the news this week, which partially solves the Erdos Discrepancy Problem. The proof was described as "bigger than Wikipedia". I attempt to explain the problem using ...

There are always two points on opposite sides of the Earth with the exact same temperature. And we can prove that.

Temperature changes continuously. If a and b are on opposite sides of the equator...

The Riemann Hypothesis is one of the Millennium Prize Problems and has something to do with primes. What's that all about? Rather than another hand-wavy explanation, I've tried to put in some detai...

The science of Star Trek has, in the past, been discussed in great detail - but what about the maths of Star Trek?

Star Trek: The Original Series contains a surprising amount of mathematics, inclu...

How many ways are there to complete a noughts and crosses board - an excuse to show you a little bit of Group Theory. Rotations, reflections and orbits - oh my!

Burnside's Lemma http://en.wikipedi...

How many ways are there to completely fill a Noughts and Crosses (tic-tac-toe) board, with four noughts and five crosses? Not including rotations and reflections.

Question sent to me by http://www...

Grime Dice juggling balls made for me by Pat Ashforth from http://www.woollythoughts.com/grimedice.html

For more information, see my video and article on Grime Dice http://grime.s3-website-eu-west...

Riemann Series Theorem may be used to show ln(2) = (1/2)*ln(2)

A formula for natural log: ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ... for |x| less than or equal to 1.

So ln(2) = 1 - 1/2 + 1/3 - 1/4...

A response to the video "Adding past infinity" by MinutePhysics http://www.youtube.com/watch?v=kIq5CZlg8Rg

Unlike convergent series, divergent series do not have limits (the sum of the first n ter...

I've made a response to Richard Wiseman's video 'How Predictable Are You' from his Quirkology Channel. The video is not here but featured on IMAmaths - the YouTube channel for the Institute of Math...

The catenary is the natural shape of a free hanging rope or chain and can be found everywhere. From the the wires of a pylon to the thread of a spider's web. From the world of bubbles to the world ...

A British couple discover the remains of a WWII carrier pigeon behind their chimney. It was carrying a coded message. Code experts believe the code used was something called a One-Time Pad Cipher, ...

Imagine a combination lock with three wheels. The wheels are labelled with the numbers 1, 2, 3. Turn the wheels and numbers increase, until 3 turns back to 1. You may only turn the first two wheels...

Before christmas I showed you some sequences called de Bruijn sequences. They're designed to contain every combination of some numbers without any repeats http://youtu.be/iPLQgXUiU14

For example, ...

Solution to the puzzle http://youtu.be/23U0X4moMCI

Three Turing videos:

Alan Turing - Celebrating the life of a genius: http://youtu.be/gtRLmL70TH0
Alan Turing and Animal Patterns: http://youtu.be/TLfRbJ_3r3g
Campaign for the Turing Tenner: http:/...

James Grime and Thomas Woolley in conversation about Alan Turing, morphogenesis and animal patterns.

Turing's original paper: The chemical basis of morphogenesis http://www.dna.caltech.edu/courses...

This year is the centenary of the birth of Alan Turing. Turing was a mathematician, father of computer science, and WWII code breaker. To celebrate his life there is a campaign to put a picture of ...

Send your entries to the Enigma Project http://enigma.maths.org Challenge ends on the 1st of March 2012.
And check out NRICH: http://nrich.maths.org (February 2012 is code month)


cipher:
VA ...

A description of how I broke the code: http://www.singingbanana.com/codechallenge2012.htm

Here's another excellent explanation from Rule The Web (http://www.youtube.com/user/rtwvidz) http://ruleth...

I have a board that uses the numbers 1 to 90. I fill the board with Othello piece, they are black on one side and white on the other. All the pieces start black side up. First I flip every second n...

The sequence 11221 contains all 2-digit combinations using the numbers 1 and 2.

A sequence such as that is called a De Bruijn sequence. I show you three methods to find such sequence. The first ...