## Articles

Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics? |
Many materials around us are oxides – such as rocks, window glass and some of the materials used in your computer. These materials may seem hard and rigid, but mathematics reveals a hidden flexibility that can explain many of their properties. |

The paths of billiard balls on a table can be long and complicated. To understand them mathematicians use a beautiful trick, turning tables into surfaces. |
Physicists love symmetry, but they get even more excited about symmetry breaking. They even believe that many of the features of the world we live in are a result of it. What do they mean by that? |

Mathematics is incredibly good at describing the world we live
in. So much so that some people have argued that maths is not just a
tool for describing the world, but that the world
is
itself a mathematical structure. Does his claim stand up to scrutiny? |
Imagine a circle with radius 1 cm rolling completely along the circumference of a circle with radius 4 cm. How many rotations did the smaller circle make? Be prepared for a surprise! |