Plus Blog

March 26, 2015

In our Researching the unknown project we explored what physicists at Queen Mary University of London get up to. As part of the project the designer Charles Trevelyan produced these four beautiful posters, which are our images of the week. Feel free to download and print them out, to adorn your classroom, bedroom or wherever you'd like to see them! Simply click on the images to download a pdf.

poster

This poster accompanies our article From dust to us.

poster

This poster accompanies our article String theory: From Newton to Einstein and beyond.

poster

This poster accompanies our article What is cosmology?

poster

This poster accompanies our article Life after the Higgs boson.

Click here to see previous images of the week.

March 18, 2015
Eclipse

A solar eclipse observed in Australia in 2012. Image: Davidfntau.

On Friday March 20, between around 9:25 GMT and 10:41 GMT, people in the UK will be able to witness a partial eclipse of the Sun! It's the first one since the total eclipse in 1999 and there won't be another one until 2026.

A solar eclipse occurs when the Moon moves in front of the Sun, blotting parts of it out and casting its shadow on the Earth. Some parts on the Earth will see a total eclipse, in which the Moon completely blocks the Sun, giving a great view of its outer atmosphere called the corona.

On Friday only a narrow path a few hundred kilometres wide will see a total eclipse. The only two landmasses in that path are the Faroe Islands and the arctic archipelago of Svalbard. In the UK the Sun will only be partially obscured to varying degrees: Edinburgh will see 93% of the Sun blotted out, Lerwick in the Shetland Isles 97%, and London 85%. In London the eclipse will start at 8:25GMT, peak at 9:31GMT and end at 10:41. Times vary slightly in other parts of the UK, with things happening earlier the further West or South you are.

Eclipse

The geometry of an eclipse. In the region called the umbra, bounded by the small yellow circle, people see a total eclipse. In the penumbra, bounded by the larger yellow circle, people see a partial eclipse.

But even when the eclipse is only partial, there are still interesting things to look out for. You might see dark spots on the Sun — sunspots — which are caused by the magnetic field of the Sun dimming its light output. You might also be able to observe the outline of the Moon's surface, with its mountains and valleys. If you're somewhere where the sunlight passes through tree foliage, you'll see lots of images of the eclipse projected on the ground and other things around you, as the holes in the foliage act as pin hole cameras.

Pinhole images on a car during the 1998 eclipse in Guadeloupe.

Pinhole images on a car during the 1998 eclipse in Guadeloupe.

It's really important that you don't look at the Sun directly, not even while it is being eclipsed, as this can seriously damage your eyes. Even sunglasses aren't good enough protection. But even if you haven't got specially produced eclipse viewing glasses, chances are there is something in your house that will help you view it. A colander and a piece of paper, for example. Standing with your back to the Sun, let the light pass through the colander onto the paper to see lots of images of the eclipsed Sun appear. You could also use a mirror to reflect the light onto a wall, or build your own pinhole camera. See this lovely booklet, produced by the Royal Astronomical Society, to find out more.

Now all we need is a clear sky!

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.

Traffic heat map

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 $\pi $ 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 $\pi $ is equal to $22/7.$ Now that is completely wrong. Writing those numbers out in decimal gives $22/7 = 3.142...$ while $\pi = 3.141...$. There’s a difference in the third decimal place after the decimal point!

Pi

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 $\pi $ 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 $\pi $, we require a value of $\pi $ 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 $\pi $.

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 $\pi $ in the order of one part in 1,000,000,000,000,000.

So, the modern world needs $\pi $ and it needs it accurately!

March 10, 2015
MM

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, far-reaching 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

Ingrid Daubechies at the opening ceremony of the International Congress of Mathematicians in 2014. Image copyright ⓒ 2010-2014 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 $(x,y)$ satisfy

  \[ x=\frac{48}{25}\sin (5t)+\frac{40}{25}\sin (6t) \]    
  \[ y=\frac{48}{25}\cos (4t)+\frac{40}{25}\cos (5t) \]    

for $\Theta \leq t \leq 2\pi -\Theta ,$ where $\Theta \approx 2.32.$ ($\Theta $ is a zero of $\frac{48}{25}\sin (5t)+\frac{40}{25}\sin (6t)$.)

The second curve consists of points in the plane whose coordinates $(x,y)$ satisfy

  \[ x=-(\sin (3t))^{3} \]    
  \[ y=\sin \left(4t+\frac{7\pi }{36}\right)-\frac{\sin \left(\frac{7\pi }{36}\right)-\sin \left(\frac{103\pi }{36}\right)}{2}(\cos (\frac{3t}{2}))^{5} \]    

for $0 \leq t \leq \frac{2\pi }{3}$.

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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