Plus Blog

April 3, 2013

The London Knowledge Lab have a fascinating Maths-Art workshop planned for this month, a "mostly" hands-on experience entitled "Art and the Möbius strip".

Animated Klein bottle

The Möbius band is one-sided (Image Konrad Polthier)

Many artists have explored the curious properties of the Möbius strip, with Max Bill and M. C. Escher among the most famous exponents. After a brief survey of this art and a basic mathematical overview, Simon Morgan and John Sharp will explore new aspects of this fascinating object as a starting point for potential new art. The session will be mainly practical because the properties of the Möbius strip can only be explored through hands-on experience. Please bring scissors, tape, and large paper sheets (e.g. old newspapers)!

The workshop is on Thursday 11th April at 6.00pm at the London Knowledge Lab, 23-29 Emerald St, London, WC1N 3QS. It is free and you don't need a ticket but an email to is appreciated to assist with planning. You can view past Maths-Art seminars on their YouTube channel and you can read more about the Möbius strip and its cousin the Klein bottle on Plus.

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March 27, 2013

The legendary mathematician Paul Erdős would have turned 100 today. Aziz S. Inan, Professor of Electrical Engineering at University of Portland and a friend of Plus, has sent us this fitting tribute.


Paul Erdős would have turned 100 today! Image: Kmhkmh.

Paul Erdős (26 March 1913-20 September 1996, died at 83) was an influential Hungarian mathematician who spent a significant portion of his later life living out of a suitcase and writing papers with those of his colleagues willing to provide him room and board. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He published more papers than any other mathematician in history, working with hundreds of collaborators. He wrote over 1,500 mathematical articles in his lifetime, mostly with co-authors. Erdős is also known for his "legendarily eccentric" personality.

Erdős strongly believed in and practiced mathematics as a social activity, having over 500 collaborators during his life. Due to his prolific output, his friends created the Erdős number as a humorous tribute to his outstanding work and productivity. The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as a measure by authorship of mathematical papers.

Today, Tuesday, 26 March 2013, marks Erdős' centennial birthday. As I was looking at numbers related to Erdős' birthday, I noticed some interesting numerical coincidences and connections. I decided to report my findings in this article, as a centennial brainteaser birthday gift for Erdős.

  • Erdős' birth date, 26 March, can be expressed in day-month date format as 26-3, or simply 263. Coincidentally, the 263rd day of 2013 and any other non-leap year is 20th of September, the day Erdős died in 1996.
  • Erdős' 100th full birthday in day-month-year date format can be written as 26-3-2013 or simply, 2632013. This number can be expressed in terms of its prime factors as follows:
      \[ 2632013=19 \times 83 \times 1669 . \]    
    So Erdős' 100th birthday expressed as 2632013 is divisible by the 263rd prime number 1669, where 263 represent Erdős' birth date, 26 March! Also, if its prime factor 1669 is split in the middle as 16 and 69, these two numbers add up to 85, where the 85th day of 2013 (and any other non-leap year) is amazingly 26 March! In addition, the prime 83 represents Erdős' death age and 19 is equal to half of the reverse of 83.
  • Erdős' birth year 1913 is the 293rd prime number, 293 is the 62nd prime number, the reverse of 62 is 26, again the day number of Erdős' birthday.
  • Erdős' 100th full birthday in month-day-year date format is 3-26-2013, or simply, 3262013. Interestingly enough, the prime factors of the reverse of 3262013 are given as follows:
      \[ 3102623 =29 \times 83 \times 1289. \]    
    Here, 1289 is the 209th prime number where 209 represents Erdős' death date, 20 September. In addition, again, prime 83 corresponds to his death age.
  • 1289 is also one of the prime factors of the reverse of Erdős' full birthday expressed in day-month-year date format as 26031913 since
      \[ 31913062 = 2 \times 1289 \times 12379. \]    

Thanks for transforming mathematics into a universal social activity through your modesty and humbleness Paul Erdős, and have a happy 100th birthday!

March 22, 2013

Want to meet some inspirational female mathematicians? Then come to the Florence Nightingale Day, a free day of activities, at Lancaster University on April 17. The day is aimed especially at girls in year 12 at schools in the Morecambe Bay and Preston areas but it is also open to boys. "Everyone talks about getting more women into mathematics but I wanted to do something to actively encourage it," says Nadia Mazza, a mathematics graduate from Lausanne University who is behind the idea. "Year 12 is a critical stage when students make crucial decisions affecting their future career plans. We want to show how appealing it can be to do maths."

Florence Nightingale

A young Florence Nightingale

Speakers at the morning session will include Professor June Barrow-Green from the Open University and pure mathematics researcher Professor Reidun Twarock, from the University of York. Opening the afternoon session will be first generation female mathematician Professor Dona Strauss from the University of Leeds. Then Beth Penrose (University of Nottingham), Fiona Murray (Principal Integrity Engineer – TA Pipelines and Structures at Centrica) and Suduph Imran (a former mathematics teacher at Our Lady's Catholic College in Lancaster who is studying for her Masters in Education) will speak about their jobs and how they use mathematics every day. Beth, Fiona and Suduph are ambassadors from STEMfirst, an organisation which promotes opportunities in science, technology, engineering and maths.

The last speaker will be one of the Plus editors, having a look at the careers of some female mathematicians.

The day will also include a hands-on mathematics contest when attendees will spend time solving tricky problems in small groups under the supervision of coaches, all PhD students from Lancaster University's Department of Mathematics and Statistics. Plus there will be displays featuring opportunities offered to women by a degree in mathematics or statistics, which will stimulate informal discussion between pupils and mathematicians.

For more information and to book places please contact Nadia Mazza at or James Groves at

The event is named after Florence Nightingale, best remembered for her work as a nurse during the Crimean War. This amazing woman had an immense love of both subjects and was a pioneer in statistics, especially in the use of visualisation of statistical data. You can find out more about her in this Plus article.

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March 21, 2013
Still Life: Five Glass Surfaces on a Tabletop

We're looking for beautiful mathematical images. Still Life: Five Glass Surfaces on a Tabletop by Richard Palais won the 2006 Science and Engineering Visualisation Challenge.

We're looking for inspiring images that illustrate your favourite mathematical ideas. Illustrations, photographs, computer simulations or even clever doodles — anything that's colourful and inspirational. The best fifty images will be used as part of a book fifty to be published by Oxford University Press to coincide with the fiftieth anniversary of the Institute of Mathematics and its Applications (IMA). The book will contain fifty examples of the best writing on mathematics, both popular and technical, aimed at a general audience. We also plan to reuse the best images (fully credited to you) in publicity for the IMA, especially its 50th Anniversary.

The idea is that these images should be able to stand alone, like pictures in an art gallery, with minimal explanation. They should ideally be approximately square or portrait style and sufficiently striking to be readable when reproduced at a size of approximately 10cm2. You need to hold the copyright for the image.

Please submit images, in low resolution at this stage, to by or before 12th May 2013, along with any appropriate explanation or attribution text. Please using the word IMAGE in the header. We encourage you to be creative!

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March 19, 2013

Here's a well-known conundrum: suppose I need to buy a book from a shop that costs £7. I haven't got any money, so I borrow £5 from my brother and £5 from my sister. I buy the book and get £3 change. I give £1 back to each my brother and sister and I keep the remaining £1. I now owe each of them £4 and I have £1, giving £9 in total. But I borrowed £10. Where's the missing pound?

The answer is that the £10 are a red herring. There's no reason why the money I owe after the whole transaction and the money I still have should add up to £10. Rather, the money I owe minus the change I got should come to the price of the book, that is £7. Giving a pound back to each my brother and sister just re-distributes the amounts. The money I still owe is reduced to £8 and the money I still have to £1. Rather than having £10-£3=£7, we now have £8-£1=£7. Mystery solved!

March 13, 2013

What a lovely coincidence! Pi day (the 14th of March, written 3.14 in the US) is also Albert Einstein's birthday. How are you going to celebrate? You could join Marcus du Sautoy and over a thousand other people in a mass online experiment to calculate pi or you could join Plus in Cambridge to watch our favourite mathematical movie Travelling Salesman. And to celebrate both the number and the man, here are some favourite articles.

How to add up quickly
One of our favourite authors, Chris Budd, takes a look at some famous infinite series involving pi and presents a trick for making them converge quicker.

Einstein as icon
In 1905 Albert Einstein changed physics forever with his special theory of relativity. Since then his name — and hair do — have become synonymous with genius. John D. Barrow looks at Einstein as a media star.

What is the area of a circle?
You might know the famous formula for an area of a circle, but why does this formula work? Tom Körner's explanation comes with a hefty estimate of pi.

What's so special about special relativity?
Most of us are aware that Einstein proved that everything was relative ... or something like that. But we go no further, believing that we aren't clever enough to understand what he did. Hardeep Aiden sets out to persuade you that they too can understand an idea as elegantly simple as it was original.

Pi not a piece of cake
Every phone number on the planet, all of our names (with the characters suitably encoded), even the works of Shakespeare can be found in the digits of pi — if these digits are truly random that is. So are they?

How does gravity work?
Einstein's theory of general relativity doesn't look at gravity as a force, rather it replaces the concept of force by that of geometry. How does that work?

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