The only good thing about a wash-out summer is that you get to see lots of rainbows. Keats complained that a mathematical explanation of these marvels of nature robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.
Airport security staff have a daunting task. With impatient queues looming over them they need to search x-ray scans of cluttered suitcases for several items at once: knives, guns and bombs. How can we ease their task and make sure they don't miss a crucial item? To find out, scientists are trying to understand how we humans take in visual information. The humble triangle plays a crucial role in the experiments they perform.
The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.