From trigonometry to waves.

Some basic trigonometry can deliver vital evidence from the scene of a crime.

Why the North Star tells you your latitude.

A little trig helps to find the relative distance to the Sun and Moon.

John D. Barrow tells us how to get the best view!

It's trigonometry's best kept secret!

Keats complained that a mathematical explanation of rainbows 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.

This teacher package brings together our material on trigonometry, from problems about simple triangles to the wavy behaviour of trig functions.

What goes up must come down — or does it? Find out how to cheat gravity with Julian Havil.

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.

We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, Chris Sangwin and Chris Budd tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time.