Plus Blog
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 191320 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 coauthors. 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.
Thanks for transforming mathematics into a universal social activity through your modesty and humbleness Paul Erdős, and have a happy 100th birthday!
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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." A young Florence Nightingale Speakers at the morning session will include Professor June BarrowGreen 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 handson 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 n.mazza@lancaster.ac.uk or James Groves at j.groves@lancaster.ac.uk. 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. 

March 21, 2013
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 10cm^{2}. You need to hold the copyright for the image.Please submit images, in low resolution at this stage, to ima50@maths.cam.ac.uk 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! 

March 19, 2013
Here's a wellknown 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 redistributes 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 Einstein as icon
What is the area of a circle? What's so special about special relativity? Pi not a piece of cake How does gravity work? 

March 7, 2013
We've been dabbling a lot in the mysterious world of quantum physics lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics. The London Velodrome's track is designed for maximum speed using Newton's laws of motion. Newton's first law: An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force. This is also called the law of inertia and it doesn't need much explanation. No stationary object will start moving of its own accord without a force being applied. And the reason why in our everyday experience moving objects tend to slow down unless they are being powered by something is due to factors such as friction and air resistance. Newton's second law: The acceleration a of a body is parallel and proportional to the net force F acting on it. The exact relationship is F=ma, where m is the body's mass. In this equation both F and a are vectors with a direction and a magnitude. Newton's third law: When two bodies exert a force on each other the forces are equal in magnitude, but opposite in direction. For every action there is an equal and opposite reaction. Thus, if you kick a ball with your foot, then the ball exerts an equal and opposite force on your foot. The three laws of motion were first published in 1687 in Newton's famous work Philosophiae Naturalis Principia Mathematica which translates as Mathematical Principles of Natural Philosophy. Newton's law of universal gravitation and mathematical techniques we'd now call calculus were also published in Principia Mathematica and together with the laws of motion they gave the first comprehensive description of the physical processes we observe in everyday life. It later turned out that the laws don't hold when you look at the world at very small scales (that's where quantum mechanics reigns) or at objects that move at very high speed or when there are very strong gravitational fields. However, Newton's laws still give a very good approximation for the physics we observe in our normal lives. To read more about Newton's laws and its applications, from understanding the melting Arctic to building the Olympic Velodrome, have a look at our teacher package on classical mechanics. 