Plus Blog

January 8, 2015

Our image of the week may look like a bird in flight...

Image by Hamid Naderi Yeganeh.

...but it’s actually a collection of points in the plane given by a mathematical formula. To be precise, it’s a subset of the complex plane consisting of points of the form

  \[ \lambda A(t)+(1-\lambda )B(t), \]    

where

  \[ A(t)= 3(\sin (t))^{3}- \frac{3i}{4}\cos (4t) \]    

and

  \[ B(t)= \frac{3}{2}(\sin (t))^{5} - \frac{i}{2}\cos (3t) \]    

for $0\leq t \leq 2\pi $ and $0\leq \lambda \leq 1.$

The image was created by Hamid Naderi Yeganeh. You can see more of Hamid's images on this website and on the American Mathematical Society website.

See here to find out more about the complex plane and here to see previous images of the week.

January 2, 2015

Charlie Stripp, Chief Executive of Mathematics in Education and Industry (MEI), has been awarded an MBE in the 2015 Queen's New Year Honours List in recognition of his services to education.

Charlie Stripp

Charlie Stripp. Image from the NCETM website.

Charlie taught mathematics for ten years in the state sector before joining MEI in 2000 to set up the pilot project that eventually became the Further Mathematics Support Programme. He became MEI's Chief Executive in 2010. Charlie is also Director of the National Centre for Excellence in the Teaching of Mathematics (NCETM), seconded from MEI on a half-time basis, and is regularly consulted by the government on mathematics education issues.

"I am delighted for my work to have been recognised with this very special honour," says Charlie. "In recent years there have been unprecedented changes in mathematics education, particularly in curriculum development and the professional development of teachers, and it has been a privilege to have been in a position to influence them."

MEI's Chairman Gerald Goodall says: "MEI plays a leading role in expanding opportunities for access to high quality mathematics education and we are very fortunate to benefit from Charlie’s leadership. MEI's trustees and staff are delighted to see Charlie's hard work and dedication recognised in this way."

Congratulations Charlie!

December 24, 2014
Kleing beer

It must almost be holidays for everyone and so it's nearly time to celebrate! For many people that involves having a nice cold glass of something and we have found the very best way to open a bottle – a beautiful Klein Bottle Opener from Bathsheba! We love Klein bottles, just one of many beautiful mathematical surfaces. You can read all about them while you enjoy your glass of bubbly!

Merry Christmas from all of us here at Plus!

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December 23, 2014
sprinter

Still have presents to buy? You'll need to be quick! To help you win the race to get those final gifts here are some mathematically sporty books by some of our favourite Plus authors!

In the brilliant Taking chances John Haigh gives a brilliant introduction to probability and its role in the lottery, quiz shows, games and all types of sport. Haigh has also written two excellent books with Rob Eastaway, How to take a penalty: The mathematical curiosities of sport and The hidden mathematics of sport.

If football in particular is the passion of your intended recipient, we recommend How to score: science and the beautiful game by Ken Bray. And for a mathematical book, filled with football inspired illustrations of mathematical ideas, there's The Num8ber My5teries by Marcus du Sautoy.

All our sport knowledge comes from our neighbour and boss, John D. Barrow, who often drops in to convey the latest mathematical news from the world of physical activity. One of our favourite stories was how he discovered a new rowing rig by analysing the maths of the ideal positioning of rowers. You can read 99 other fascinating facts in his book 100 Essential Things you didn't know you didn't know about sport.

And of course, you can read more about the mathematics of sport on Plus and the Sportal.

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December 21, 2014

"A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas."

Scene from the play

Shane Shambhu as Ramanujan and David Annan as Hardy in the play A disappearing number. Photo: Tristram Kenton.

This beautiful sentence is from G.H. Hardy's 1940 essay A mathematician's apology. The work was Hardy's attempt to justify the pursuit of pure maths to non-mathematicians and to explain its motivation. It focuses on the beauty of maths and, unlike many other attempts to make maths appear attractive, takes pride in the un-applicability of pure maths — partly because something that has no applications can't do any harm. It's an understandable sentiment for a pacifist like Hardy at the time of WWII. And although Hardy was proved very wrong about the "purity" of his own field, number theory, which is today used in cryptography, it's still a fascinating and thought-provoking read.

In the Apology Hardy also mentions the mathematician Srinivasa Ramanujan, who played a defining part in Hardy's mathematical life:

"I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, 'Well, I have done one the thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.'"

Hardy's collaboration with the self-taught Indian genius was remarkable. It inspired the 2008 play, A disappearing number, which we explored in this Plus article. You can also listen to our podcast with actor and mathematician Victoria Gould reading a section from the foreword to Hardy's Apology.

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December 19, 2014
Ramanujan

Srinivasa Ramanujan (1887 - 1920).

December 22nd would have been the 127th birthday of the legendary Indian mathematician Srinivasa Ramanujan. His story really is remarkable. Born in 1887 in a small village around 400km from Madras (now Chennai), Ramanujan developed a passion for maths very early on. By age 15 he routinely solved maths problems that went way beyond what his classmates were dealing with. He worked out his own method for solving quartic equations, for example, and even had a go at quintic ones (and failed of course, since the general quintic is unsolvable). But since he neglected all other subjects apart from maths, Ramanujan never got into university, and was forced to continue studying maths alone and in poverty. Only after a plea to an eminent mathematician, who described Ramanujan as "A short uncouth figure, stout, unshaven, not over clean," did Ramanujan eventually get a job as a clerk at the Madras Port Trust.

It was during his time at the Port Trust that Ramanujan decided to write a letter that was to change his life. It was addressed to the famous Cambridge number theorist G. H. Hardy who, accustomed to this early-twentieth-century form of spam, was irritated at first: a letter from an unknown Indian containing crazy-looking theorems and no proofs at all. But as he went about his day, Hardy couldn't quite forget about the script:

At the back of his mind [...] the Indian manuscript nagged away. Wild theorems. Theorems such as he had never seen before, nor imagined. A fraud of genius? A question was forming itself in his mind. As it was Hardy's mind, the question was forming itself with epigrammatic clarity: is a fraud of genius more probable than an unknown mathematician of genius? Clearly the answer was no. Back in his rooms in Trinity, he had another look at the script. He sent word to Littlewood that they must have a discussion after hall...

Apparently it did not take them long. Before midnight they knew, and knew for certain. The writer of these manuscripts was a man of genius.

From the foreword by C. P. Snow to Hardy's A Mathematician's Apology


Hardy invited Ramanujan to Cambridge, and on March 17, 1914 Ramanujan set sail for England to start one of the most fascinating collaborations in the history of maths. Right from the start the pair produced important results and Ramanujan made up for the gaps in his formal maths education by taking a degree in Cambridge. Perhaps the most famous story to emerge from this period has Hardy visiting Ramanujan as he lay ill in bed. Hardy complained that the number of the taxi he had arrived in, 1729, was a boring number, and that he worried this was a bad omen. "No," Ramanujan replied, apparently without hesitation. "It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways":

  \[ 1729 = 1^3 + 12^3 = 9^3 + 10^3. \]    

Unfortunately, Ramanujan's sickness wasn't a one-off. His health had always been feeble, and the cold weather and unaccustomed English food didn't help. Ramanujan decided to return to India in 1919 and died the following year, aged only 33. He is still celebrated as one of India's greatest mathematicians.

You can find out more about Ramanujan's mathematics in these Plus articles:

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