Plus Blog

September 16, 2014

Mr and Mrs Huntrodd were both born on the same day — 19 September 1600. That's quite a coincidence isn't it? (See here just how much of a coincidence this is.) What's even more of a coincidence is that they both died, within 5 hours of each other, on the same day too, which was… drum roll please… 19 September 1680! This seems very surprising. So surprising that even the very hard to surprise Professor Sir David Spiegelhalter OBE, Winton Professor of the Public Understanding of Risk and friend of Plus, was surprised. So surprised that he took this photo and is now throwing a party to celebrate this unlikely event with party, this Friday 19 September.

tomb

(Image by David Spiegelhalter, image licensed under Creative Commons)

You can join Spiegelhalter and his risky colleagues Timandra Harkness and Michael Blastland at their Huntrodd's party or you can throw your own. Visit the website to find out more! Happy Huntrodd's day!

You can read more about coincidence in Spiegelhalter's Plus column or the Understanding Uncertainty site.

September 11, 2014

We have several images of the week this week! And they all come from the beautiful design for the new maths gallery that will open at the Science Museum in London in 2016. The first is the inspiration that Zaha Hadid Architects used for the layout of the gallery. It's the turbulence field of an aircraft which captures how the air moves around it. This is mathematically described by the Navier Stokes equations, which apply in many different situations, from modelling the weather to understanding how blood flows. (You can read more about the Navier Stokes equations in Universal pictures and turbulence in Understanding turbulence.)

MathsGalleryLayout

A top view of the turbulence field around the Handley Page aircraft, one of the main exhibits in the new maths gallery (Image courtesy of Zaha Hadid Architects)

Handley Page Gugnunc

The Handley Page Gugnunc in flight

The plane that will hang in the centre of the gallery is a Handley Page Gugnuncs. This experimental plane was designed for the Guggenheim Safe Aircraft competition in 1929 which aimed to find planes that could fly safely at slow speeds and with short takeoffs. The research beind the plane profoundly advanced aviation technology and understanding at the very beginnings of civilian air travel. (You can read two brilliant articles from the 1930s about the competition and the aircraft itself.)

Behind the plane are three minimal surfaces (surfaces with the smallest possible area that satisfy some constraints) that are based on the shapes of the vortices in the turbulence created behind the plane in flight. The equation defining these
  \[  \begin{array}{l} a_1 sin(x)sin(2y)sin(3z) \\ + a_2 sin(2x)sin(y)sin(3z)\\ +a_3 sin(2x)sin(3y)sin(z)\\ +a_4 sin(3x)sin(y)sin(2z)\\ +a_5 in(x)sin(3y)sin(2z)\\ +a_6sin(3x)sin(2y)sin(z)=0 \end{array}  \]    
The plane exhibit

The design or the Handley Page exhibit in the new maths gallery

is a complicated looking combination of familiar sine functions that is governed by six different parameters. By varying the values of these parameters, the $a_ i$, the surface bends and twists producing a whole family of different shapes. Some of these will be created will be created in physical form to provide the support display cases used throughout the galleries. You can play with these surfaces yourself or just watch their creation in the video below.

It is thrilling to see such a striking, beautiful and mathematical design for the gallery. But of course the real strength will be the exhibits themselves. These will span 400 years of science and mathematics with objects ranging from hand-held mathematical instruments from the renaissance to modern technology. We all know that maths is the language of the universe and we can't wait to see what stories we'll find in the new maths gallery when it opens in 2016.

You can find out more about the gallery at the Science Museum

September 9, 2014
Helen Mason and students from AIMSSEC

Cambridge solar physicist Helen Mason with South African students during her 2005 trip to AIMSSEC.

Later this month you get a chance to enjoy beautiful music twice as much as normal: not only will you hear the wonderful voices of the Adventist Vocal Ensemble, you will also also be helping to empower disadvantaged children in Africa through the power of maths education.

The African Institute for Mathematical Sciences Schools Enrichment Centre (AIMSSEC) founded in 2003, is a not-for-profit organisation empowering teachers to make an important difference to the educational opportunities of many thousands of South African children, and also to train other teachers. Experts from universities across the world, work as unpaid volunteers, with the African staff, to give professional development courses for mathematics teachers, subject advisers and field trainers working in disadvantaged rural and township communities, improving their subject knowledge and teaching skills and providing resources. AIMSSEC's work extends to other African countries and continues to grow and expand in the interest of sustainable improvement of education in Africa.

The concert, Rise Up for Africa, will raise funds for bursaries for some of the many hundreds of teachers in disadvantaged communities who are keen to attend the courses, yet have no funding to do so. AIMSSEC have raised enough funds for 7 teachers to attend the courses so far and their objective is that the Rise Up for Africa Benefit Concert will enable another 20 teachers to attend by raising £10,000.

Rise Up for Africa is at 7pm Saturday 27 September at All Saints Haggerston Church Hackney, London E8 4EP. You can find out more information and book your tickets here.

September 5, 2014
Double pendulum

Image by Michael G. Devereux.

This week's striking image is a long exposure photograph of a double pendulum by Michael G. Devereux. Double pendulums provide a striking physical illustration of chaotic behaviour, captured in this image by attaching LEDs to each part of the pendulum. You can read more about chaotic behaviour in this and other systems in Finding order in chaos.

The picture is one of the images that appears in the book 50 visions of mathematics, which celebrates the 50th anniversary of the Institute of Mathematics and its Applications.

You can see previous images of the week here.

September 4, 2014
Ruler

Adding fractions is probably the first difficult bit of maths we come across at school. For example, to work out $\frac{5}{6} + \frac{7}{10}$ you first need to figure out that the lowest common multiple of 6 and 10 is 30, and that in order to get 30 in the denominator of both fractions you need to multiply the numerator 5 by 5 and the numerator 7 by 3. This gives

$\frac{5}{6} + \frac{7}{10} = \frac{(5 \times 5)}{30} + \frac{(7 \times 3)}{30} = \frac{25}{30} + \frac{21}{30} = \frac{(25+21)}{30} = \frac{46}{30}.$

You then need to get rid of the common factors of 46 and 30, giving the final result $\frac{23}{15},$ which bears no resemblance whatsoever to the original two fractions. Doing this as a ten-year-old who has never seen it before is pretty tough.

Here is an alternative recipe that always works and doesn't involve faffing around with lowest common denominators. Writing "top" for numerator and "bottom" for denominator, the idea is to do:

(top left x bottom right + top right x bottom left) / (bottom left x bottom right).

Applied to our example this gives:

  \[  \frac{(5 \times 10 + 7 \times 6)}{(6 \times 10)} = \frac{(50 + 42)}{60} = \frac{92}{60} = \frac{23}{15}.  \]    

The difference to the standard way of adding fractions is that you are not bothered with finding the lowest common denominator. You simply use the product of the two denominators as a common denominator. Then, in order to bring both fractions on that common denominator you only need to multiply the numerator of each by the denominator of the other. Easy!

Apparently this is how Vedic mathematicians in ancient India added up fractions. If you happen to speak German, you can also explore this method in musical form in this maths rap by DorFuchs. And even if you don't speak German, it's cute!

11 comments
August 29, 2014
Vortex

Image by Ole Myrtroeen and Gary Hunt.

This vortex looks so friendly, we made it our image of the week! It was formed in a physical experiment in which a saline solution (stained blue) was ejected upwards into a still fresh-water environment. The image was produced by Ole Myrtroeen and Gary Hunt, University of Cambridge, and appeared on the cover of vol. 657 of Journal of Fluid Mechanics, © Cambridge University Press.

The picture is one of the images that appears in the book 50 visions of mathematics, which celebrates the 50th anniversary of the Institute of Mathematics and its Applications.

You can see previous images of the week here.

Syndicate content