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.

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

What happens when a procedure calls itself?

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

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

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

Turn through bigger angles and draw stars with Logo.

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.

Learn about Pen Up and Pen Down in Logo

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

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

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

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

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

Make some celtic knot patterns using tiling techniques

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

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?

How efficiently can various flat shapes be fitted together?

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?

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

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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

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?

A game in which players take it in turns to choose a number. Can you block your opponent?

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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

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