Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.

In the 1950's, Ernst Straus asked a seemingly simple problem. Imagine a dark room with lots of turns and side-passages, where all the walls are covered in mirrors - just like the Hall of Mirrors in an old-fashioned fun-fair. Is it true that if someone lights a match somewhere in the room, then wherever you stand in the rest of the room (even down a side-passage) you can see a reflection of the match?

Here's how you can make your own cross-shaped boomerang - and it's safe enough to fly indoors! Hugh rolls up his sleeves and proves that theory isn't everything.

In this article, we look at the physics behind the curved flight path of a returning boomerang, and explain that boomerangs are really a kind of gyroscope. We even show you how to bang up a boomerang yourself!

Whatever is so wonderful about point B that makes all the people at point A want to get there? Robert Hunt sits at point C, and muses on the problem.

If boomerangs are really gyroscopes, then what are gyroscopes? In this article, we explore some more of the physics of gyroscopes, and demonstrate some interesting experiments you can do with them.

Starting in this issue, PASS Maths is pleased to present a series of articles about proof and logical reasoning. In this article we give a brief introduction to deductive reasoning and take a look at one of the earliest known examples of mathematical proof.

Bisecting a given angle using only a pair of compasses and a straight edge is easy. But trisecting it - dividing it into three equal angles - is in most cases impossible. Why?

Computer games and cinema special effects owe much of their realism to the study of fractals. Martin Turner takes you on a journey from the motion of a microscopic particle to the creation of imaginary moonscapes.

The term fractal, introduced in the mid 1970's by Benoit Mandelbrot, is now commonly used to describe this family of non-differentiable functions that are infinite in length. Find out more about their origins and history.

Practical problems often have no exact mathematical solution, and we have to resort to using unusual techniques to solve them. From navigation in the 17th century to postage stamps, see how this principle applies to a variety of real-life problems - and also learn how to use a piece of string to locate a German bomber!