Clever geometry produces materials that shrink when heated.

Remember how hard it was to fold maps? Mathematicians have struggled with map folding problems for ages but a recent insight suggests there might be another way to approach them, making an unlikely connection between combinatorics, origami and engineering.

Africa isn't a continent that's famous for cutting edge research. But at the University of Stellenbosch, 50km East of Cape Town, South Africa, Kiran Dellimore and his team are engineering medical equipment that will save the lives of people all over the world. Latest projects include replacement heart valves made from kangaroo tissue and equipment to help resuscitate people in emergencies.

Compass & Rule: Architecture as Mathematical Practice in England, 1500-1750, is a lovely online version of the physical exhibition help at the Museum of the History of Science, Oxford, in 2009. Compass and Rule focuses on design and drawing, exploring the role of geometry in the dramatic transformation of English architecture between the 16th and 18th centuries.

The dome of St Paul's, rising elegantly above London since the cathedral was rebuilt late in the seventeenth century, hides an intriguing early example of the interplay between maths and architecture.

Looking out to Canary Wharf, to the arch at Wembley Stadium, and down onto the Gherkin, the 700 people working on the construction site of the Heron Tower in London had one of the best views in London. Plus was lucky enough to speak to two engineers involved in building the tower and asked how maths was involved in the construction of such an impressive addition to the London skyline.

The Velodrome, with its striking curved shape, was the first venue to be completed in the London Olympic Park. Plus talks to structural engineers Andrew Weir and Pete Winslow from Expedition Engineering, who were part of the design team for the Velodrome, about how mathematics helped create its iconic shape.

This summer the Royal Institution is running a series of workshops as part of its Engineering Week where you will have a chance to try your hand at engineering and discover it is rocket science, underwater robotics, hip joint design, crash testing and much more!