A description of how to make the five Platonic solids out of paper.
Which of the following cubes can be made from these nets?
Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Make an equilateral triangle by folding paper and use it to make
patterns of your own.
Make a cube with three strips of paper. Colour three faces or use
the numbers 1 to 6 to make a die.
What happens when a procedure calls itself?
Write a Logo program, putting in variables, and see the effect when you change the variables.
How many differently shaped rectangles can you build using these
equilateral and isosceles triangles? Can you make a square?
More Logo for beginners. Now learn more about the REPEAT command.
Turn through bigger angles and draw stars with Logo.
Learn about Pen Up and Pen Down in Logo
Make a ball from triangles!
Make a clinometer and use it to help you estimate the heights of
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
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.
These are pictures of the sea defences at New Brighton. Can you
work out what a basic shape might be in both images of the sea wall
and work out a way they might fit together?
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
Make a spiral mobile.
A game to make and play based on the number line.
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Follow these instructions to make a three-piece and/or seven-piece
This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.
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?
This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.
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.
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
Can you describe what happens in this film?
These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
Learn to write procedures and build them into Logo programs. Learn to use variables.
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.
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
The challenge for you is to make a string of six (or more!) graded cubes.
Here's a simple way to make a Tangram without any measuring or
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Here is a chance to create some Celtic knots and explore the mathematics behind them.
Did you know mazes tell stories? Find out more about mazes and make
one of your own.
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
How is it possible to predict the card?
Surprise your friends with this magic square trick.
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
How can you make an angle of 60 degrees by folding a sheet of paper