## Shapes: Looking at Tessellation

Tessellation is the covering of a surface with repeating patterns of regular or irregular shapes that fit together exactly (interlock), with no gaps or overlaps. The earliest tessellations discovered date from the Sumerian civilisation, in about 4000 BC, where tessellations of clay tiles were used as decoration on walls and …

## Measuring Slopes: Make a Clinometer

A clinometer (also known as a declinometer or inclinometer) is used to measure the steepness of a slope, and can be used to work out the heights of tall things, such as buildings or trees. Making a Clinometer Take a plastic 180-degree protractor, and make a small hole where the …

## The Golden Section

The golden ratio (also known as the golden section or golden mean, or as the Greek letter ‘phi’) describes a rectangular shape that people find an attractive shape, particularly in art or architecture. No-one is quite sure why this is a particularly pleasing shape, but it appears to be something …

## A Fractal Pattern

A fractal is a pattern that repeats itself, getting smaller and smaller each time. Each part of the pattern looks like a smaller version of the whole thing. A tree trunk splits up into branches – these then split up into smaller and smaller branches and then twigs. This is …

Maths can’t really reveal the secret of telepathy (reading people’s minds), but some clever maths tricks make it seem like it is possible. Some of these will need a calculator. Examples are in square brackets but try them with other numbers and read people’s minds! The Answer is Three Think …

## Get Knotted: Learn About Topology

Knot theory is the study of knots. As well as being useful to hold things together, knots and knot theory are important in different areas of science, including biology and chemistry. Why are Knots Useful? Knots have been used all the way through the history of humans – archaeologists have …

## Calculating Pi

Pi is a number used in maths used to work out the circumference of a circle (the distance around the outside) or the radius (the distance from the edge of a circle to the centre), and is called a ‘mathematical constant’, a number used in maths that does not change …

## How Many Surfaces? Making a Möbius Strip

A Möbius strip is a loop of paper with a twist in it, that behaves in a very odd way. How to Make a Möbius Strip Take a strip of paper, curve it round into a loop and glue the ends together. Draw a line all the way around the …

## How Tall is It? Measure Something Tall Without Climbing It

The most accurate way to measure something is using a tape measure, but some things are too tall (or too scary) to climb with a ruler. Try the different methods for the same tree and see how similar (or different) the results are. These examples are all about trees, but …

## Make a Right Angle With Knots and String

A right angle is a square-shaped or L-shaped angle, and measures 90 degrees (a quarter of a circle). A square is made up of four right angles. Make a Right Angle with Knots and String Find a long piece of string and tie 13 knots in it. It doesn’t matter …