A thumbnail catalogue of current designs and colour variants – click on an illustration for a larger version. Click on a section heading to see background information for that particular design.

**Multiplication in algebra**

Drawing a diagram of an algebraic multiplication can often demystify the process.

# What is a derivative?

This simple, elegant design illustrates a crucial and revolutionary discovery in mathematics – the derivative and its close cousin, the infinitesimal calculus.

**The Fibonacci series**

A visual exploration of a strange sequence of numbers that crops up in the most unlikely places.

**Fractal rectangle & Koch star**

Some of the fascinating qualities of fractals are displayed in the increasingly complex rectangle of this design.

**Golden ratio circles**

Another example of a design springing from my fascination with the Fibonacci series. In a simple design which can be created using nothing more that a ruler and compass, we explore strange values like the square root of 5 and the legendary ‘golden ratio’.

**Nautilus based on square roots**

Complex structures and difficult numbers can often be based on simple actions, as this elegant shape illustrates.

# The nine point circle

A surprising and neat result anyone can obtain using nothing more than a ruler and compass.

**One ring to rule them all**

Draw three points on a piece of paper. How many circles can you draw which take in all three points. One, and one only. And this design illustrates why.

This design is a little bit of fun but it also has serious purpose. It shows that the use of simple diagrams can help to clarify an idea that words have confused. They could be described as Venn diagrams except that they are so simple that they make no real use of the special qualities of John Venn’s invention, which dates from the 1880s.

It also serves to illustrate the way the vital word ‘if’ is used in mathematical thinking.

**Pi me a river**

There’s a surprising relationship between the length of rivers and the strange number we call *pi*.

**Pi sticks**

A few lines on a piece of paper and a needle are enough to begin calculating the mysterious value ‘pi’.

**Primes in 1000**

Patterning prime numbers, the building blocks on which all other numbers are based.

**Primes in a hexagon**

Another in the series exploring different ways of presenting prime numbers visually.

**Proof of Pythagoras**

You probably know Pythagoras’ Theorem, but could you describe how it works? With this design on the wall, you soon will.

**Rectangles in a Triangle**

An apparently simple problem leads to some tricky questions.

**Sin, cos and tan waves**

For many years I found those curves that appeared on the old oscilloscopes a slippery thing. How were they ‘sine waves’ and what on earth did it mean when people said that two wave forms were ’90 degrees out of phase’.

It helped when it first dawned on me what simple concepts sines and cosines actually were. But still… ’90 degrees out of phase’?

So I like this design for its liveliness, for the neatness of the concept embodied in the small icons and, not least, because when I look at it sets my mind at rest.

**Sines and cosines**

When something is widely used, often in dense and complex expressions, it can be easy to forget that it’s actually very simple. So it is with sines and cosines

**The Sieve of Eratosthenes**

An ancient method of finding prime numbers that is still in use today.

**Triangles and squares**

Demystifying square numbers.