## Plus Blog

March 22, 2013
Want to meet some inspirational female mathematicians? Then come to the 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 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 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 |
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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 ^{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! |
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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! |
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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
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? |
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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.
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.
In this equation both
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 |
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February 19, 2013
Solving equations often involves taking square roots of numbers and if you're not careful you might accidentally take a square root of something that's negative. That isn't allowed of course, but if you hold your breath and just carry on, then you might eventually square the illegal entity again and end up with a negative number that's a perfectly valid solution to your equation. People first noticed this fact in the 15th century. A lot later on, in the 19th century, William Rowan Hamilton noticed that the illegal numbers you come across in this way can always be written as where and are ordinary numbers and stands for the square root of The number itself can be represented in this way with and Numbers of this form are called complex numbers. You can add two complex numbers like this: And you multiply them like this: The complex number But how can we visualise these numbers and their addition and multiplication? The and components are normal numbers so we can associate to them the point with coordinates on the plane, which is where you get to if you walk a distance in the horizontal direction and a distance in the vertical direction. So the complex number which is the sum of and corresponds to the point you get to by walking a distance in the horizontal direction and a distance in the vertical direction. Makes sense. What about multiplication? Think of the numbers that lie on your horizontal axis with coordinates Multiplying them by flips them over to the other side of the point : goes to goes to and so on. In fact, you can think of multiplication by as a rotation: you rotate the whole plane through 180 degrees about the point Multiplying by What about multiplication by the square root of ? Multiplying twice by is the same as multiplying by So if the latter corresponds to a rotation through 180 degrees, the former should correspond to rotation by 90 degrees. And this works. Try multiplying any complex number, say by and you will see that the result corresponds to the point you get to by rotating through 90 degrees (counter-clockwise) about And what about multiplying not just by but by a more difficult complex number Well, multiplying by an ordinary positive number corresponds to stretching or shrinking the plane: multiplication by 2 takes a point to which is further away from (that’s stretching) and multiplication by 1/2 takes it to which is closer to (shrinking). Multiplying by 2 is stretching. It turns out that multiplication by a complex number corresponds to a combination of rotation and shrinking/stretching. For example, multiplication by is rotation through 120 degrees followed by stretching by a factor of 2. So complex numbers are not just weird figments of the imagination designed to help you solve equations, they’ve got a geometric existence in their own right. You can find out more about complex numbers and things you can do with them in the |