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.

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?

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

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.

Learn about Pen Up and Pen Down in Logo

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

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?

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

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?

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

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

Use the tangram pieces to make our pictures, or to design some 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.

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. . . .

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

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

A game to make and play based on the number line.

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

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

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

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

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.

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

Surprise your friends with this magic square trick.

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

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

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

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.

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

What happens when a procedure calls itself?

Turn through bigger angles and draw stars with Logo.

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

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

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.

Make some celtic knot patterns using tiling techniques

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

Make a mobius band and investigate its properties.

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.

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

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?

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

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?