# Articles

Galloping gyroscopesIf 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.
The origins of proofStarting 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.
Mathematical Mysteries: Trisecting the AngleBisecting 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?
Editorial
• Roll-over malevolence
• Time to change
• Understanding science
Modelling nature with fractalsComputer 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 origins of fractalsThe 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.
Pilgrims, planes and postage stampsPractical 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!
Mathematical mysteries: the three body problem

On June 25th 1998 the Solar and Heliospheric Observatory known as SOHO, a small spacecraft that monitors the sun, went missing. An error in the instructions given to it from ground control left it spinning out of control. However, there is a glimmer of hope.

EditorialTesting times
What computers can't doMike Yates looks at the life and work of wartime code-breaker Alan Turing. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.
Light's identity crisisWhat is light? Sometimes it seems wave-like and sometimes particle like. See how Einstein applied his theory of relativity to the problem, predicted that photons have no mass and laid the foundations for quantum mechanics.
Quantum uncertaintyQuantum mechanics is the physics of the extremely small. With something so far outside our everyday experience it's not surprising to find mathematics at the heart of it all. But at the quantum scale nothing in life is certain... Peter Landshoff explains.