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

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

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

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.

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

Learn to write procedures and build them into Logo programs. Learn to use variables.

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

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

Turn through bigger angles and draw stars with Logo.

What happens when a procedure calls itself?

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

Learn about Pen Up and Pen Down in Logo

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

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

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

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

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.

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

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Follow these instructions to make a three-piece and/or seven-piece tangram.

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Make a mobius band and investigate its properties.

Make some celtic knot patterns using tiling techniques

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

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Surprise your friends with this magic square trick.

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?

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

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. . . .

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

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

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

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.

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?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

A jigsaw where pieces only go together if the fractions are equivalent.

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

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

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

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

Build a scaffold out of drinking-straws to support a cup of water

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?

Which of the following cubes can be made from these nets?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.