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

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

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

Turn through bigger angles and draw stars with Logo.

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.

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

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

What happens when a procedure calls itself?

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

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

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.

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

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

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

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

Make some celtic knot patterns using tiling techniques

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?

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

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. . . .

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.

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

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

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

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

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?

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

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

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

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?

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

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?

Use the tangram pieces to make our pictures, or to design some of your own!

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

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

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

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

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

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.

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?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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