Plus Blog
March 17, 2015
Were you stuck in traffic on your way to work or school this morning? Then you might take consolation in the thought of yourself as a tiny experimental subject in the giant petri dish of the UK's motorways, contributing your data points to a greater understanding of traffic flow. Our image of the week shows a heat map of the traffic on a clockwise section of the M25 (junction 9 to junction 14) showing the speed of cars as a colour, from pale yellow for around 80 mph to red for stationary, as they pass along this stretch of road on a typical Monday. The image was created by Richard Gibbons, from the University of Cambridge's Computer Laboratory. It is based on data collected by the Highways Agency from MIDAS (the Motorway Incident Detection and Automatic Signalling) system, archived minute by minute since 1997 at loop detectors every few hundred metres under many UK motorways. The diagonal red stripes streaking down the image from the left to right between 7am and 11am are driver's commuting pain manifested in data. A driver's path through the data will start at the bottom and move upwards as they passed along the motorway and to the right as time passed. And if they passed junction 9 at, say, 7.30 in the morning, they would have hit red stripe after red stripe, like striking the incoming wave fronts as you try to swim out from a beach. These stripes are the wave fronts of a stop and go wave, the infuriating pattern of repeated stopping (red) and starting (yellow) that is well known to both motorists and traffic modellers. This is a kind of shock wave that moves back through the traffic, opposite to the direction the cars are travelling. This can be easily seen in the heat map: one starts around junction 12 and moving backwards down the motorway as time goes on. Click here to see previous images of the week. 

March 14, 2015
Today, written as 3/14 the American way, is day! This special day happens every year, but today is extra special! It’s 3/14/15, giving us the first five digits of that lovely number, rather than just three! But why should we care about all these digits? If you had a sloppy maths teacher at school you might have grown up with the idea that the number is equal to Now that is completely wrong. Writing those numbers out in decimal gives while . There’s a difference in the third decimal place after the decimal point! How accurately do we need to know the value of π? Surely this small inaccuracy doesn't matter? Well, as the following extract from a longer article by Chris Budd shows, it really does. The point is that is not any number. It lies at the heart of any technology that involves rotation or waves, and that is much of mechanical and electrical engineering. If rotating parts in, say, a typical jet engine are not manufactured to high tolerance, then the parts simply won’t rotate. This typically involves measurements correct to one part in 10,000 and, as these measurements involve , we require a value of to at least this order of accuracy to prevent errors. In medical imaging using CAT or MRI scanners, the scanning devices move on a ring which has to be manufactured to a tolerance of one part in 1,000,000, requiring an even more precise value of . However, even this level of accuracy pales into insignificance when we look at modern electrical devices. In high frequency electronics, with frequencies in the order of 1GHz (typical for mobile phones or GPS applications), electrical engineers require a precision in the value used for in the order of one part in 1,000,000,000,000,000. So, the modern world needs and it needs it accurately! 

March 10, 2015
Maryam Mirzkhani, the first female Fields medallist We may be a little late in celebrating International Women's Day but it's not for a shortage of excellent female mathematicians to celebrate! Here are some of the most inspiring women we've worked with or learnt about in the last year... Maryam Mirzakhani is one of the best mathematicians in the world. Last August she received the Fields medal (one of the highest accolades in mathematics), recognised for her "rare combination of superb technical ability, bold ambition, farreaching vision, and deep curiosity". She was the first woman to be awarded this prize and we were lucky enough to meet Mirzakhani and learn about her fascinating work in topology at the International Congress of Mathematicians (ICM) in Seoul last Summer. Ingrid Daubechies at the opening ceremony of the International Congress of Mathematicians in 2014. Image copyright ⓒ 20102014 International Congress of Mathematicians 2014, all rights reserved. At the ICM we were also fortunate to meet Ingrid Daubechies, President of the International Mathematical Union. As well as talking to her about the importance of a mathematical community, we heard her speak about her recent work virtually restoring paintings, just one application of wavelet theory. Famously it has also been used by the FBI to digitise finger prints, and it is widely used in medical imaging. Debauchies made fundamental discoveries in wavelet theory that opened up the field and has had an important role in making this mathematics into a practical tool for analysis in other areas outside mathematics. (You can read more about wavelets and how Debauchies work opened up this field here.) We also found out about a fantastic mathematician, Margharita Piazolla Beloch, who discovered a new type of origami fold (the sixth axioms of origami) in 1936 and proved that this fold solves cubic equations. We'll write more about Beloch in upcoming articles, but it's thanks to her discovery that we can now solve the unsolvable and trisect an angle. And finally, one of the people we've really enjoyed working with this last year (and years before that!) is Vicky Neale, our former colleague and now Whitehead Lecturer at the Mathematical Institute in Oxford. As well as learning many fascinating things working with Vicky on a project producing new and exciting resources for sixth form students, we've also really enjoyed listening to Vicky's contributions to many radio shows and her popular lectures and workshops. You can listen to many of her recordings online, the details are here. 

February 26, 2015
If you feel in need of some love this cold, dark February, then our images of the week might be just what you need. These hearts, created by Hamid Naderi Yeganeh, aren't drawn by hand, but defined by mathematical equations. Image by Hamid Naderi Yeganeh. Image by Hamid Naderi Yeganeh. The first curve consists of points in the plane whose coordinates satisfy for where ( is a zero of .) The second curve consists of points in the plane whose coordinates satisfy for . You can see more of Hamid's images on this website, in The Guardian and on the American Mathematical Society website. Click here to see previous images of the week.
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February 25, 2015
The Cambridge Science Festival will kick off on March 9, and there is some great maths in the programme. Here are some mathsrelated events we are particularly excited about (in chronological order). Click on the links for price, booking and location information. For the full programme visit the festival website. And if you can't make it to Cambridge, then read the Plus articles by some of the speakers, linked to from the individual entries.


February 9, 2015
This short video features one of our favourite mathematicians, Corinna Ulcigrai from the University of Bristol, talking about mathematical billiards, its connection to chaos theory, and why mathematicians study it. You can also read our article Chaos on the billiard table, based on an interview with Ulcigrai. This video was originally produced for the Cambridge Mathematics Education Project.
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