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.

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 appear 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.

Adding fractions is probably the first difficult bit of maths we come across at school. For example, to work out 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

You then need to get rid of the common factors of 46 and 30, giving the final result 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:

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!

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 appear 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.

From intelligent machines and animal emotions to phones that can detect illness — find out how mathematics shapes our world!

As we attempt to close our overstuffed suitcases for the flight home, we are very pleased that Plus too is overflowing with goodies from this years International Congress of Mathematicians in Seoul.

From the excitement of the announcement of the Fields medallists to meeting mathematicians from around the world, we've had a brilliant time. We've still got a few articles and podcast yet to publish, but for now, you can find all our coverage from ICM 2014 here.

Thank you to all mathematicians for their talks and to those who generously gave their time for interviews and explanations. A huge thank you to the local organisers of the conference, the staff at the media office and the many enthusiastic and helpful volunteers who made the event such a success. Thank you!