Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

What shape and size of drinks mat is best for flipping and catching?

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

Make an equilateral triangle by folding paper and use it to make patterns of your own.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Learn about Pen Up and Pen Down in Logo

More Logo for beginners. Now learn more about the REPEAT command.

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

What shape is made when you fold using this crease pattern? Can you make a ring design?

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Turn through bigger angles and draw stars with Logo.

How can you make a curve from straight strips of paper?

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

This activity investigates how you might make squares and pentominoes from Polydron.

Write a Logo program, putting in variables, and see the effect when you change the variables.

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

Here is a chance to create some Celtic knots and explore the mathematics behind them.

A description of how to make the five Platonic solids out of paper.

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Use the tangram pieces to make our pictures, or to design some of your own!

This article for students gives some instructions about how to make some different braids.

What happens when a procedure calls itself?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

An activity making various patterns with 2 x 1 rectangular tiles.

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?