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.

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?

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?

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

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

Make a mobius band and investigate its properties.

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

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

Surprise your friends with this magic square trick.

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

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

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

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?

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.

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

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

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

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

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.

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 some celtic knot patterns using tiling techniques

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

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

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?

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

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. . . .

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.

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

Learn about Pen Up and Pen Down in Logo

What happens when a procedure calls itself?

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

Turn through bigger angles and draw stars with Logo.

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

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

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.

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

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.

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?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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

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?

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?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?