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

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.

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.

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

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?

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

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

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?

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

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

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

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

Make a mobius band and investigate its properties.

Make some celtic knot patterns using tiling techniques

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.

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

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. . . .

What happens when a procedure calls itself?

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

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

Turn through bigger angles and draw stars with Logo.

Learn about Pen Up and Pen Down in Logo

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

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.

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.

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

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

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

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

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

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

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

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

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

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?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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

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

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

Follow these instructions to make a five-pointed snowflake from a square of paper.

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?