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.

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

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

Turn through bigger angles and draw stars with Logo.

Make a clinometer and use it to help you estimate the heights of tall objects.

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

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

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

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

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

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

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.

What happens when a procedure calls itself?

Learn about Pen Up and Pen Down in Logo

Make a mobius band and investigate its properties.

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.

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.

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?

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?

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

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.

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

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?

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

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?

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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.

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

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

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

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

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

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

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

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

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?

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.

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