Skip over navigation
Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Making Maths: Make a Magic Circle
Make a Magic Circle - a never-ending, one-sided shape
You will need
A sheet of paper - A4 or A3
A pair of scissors
Sellotape or Scotch tape
What to do
Cut a long, thin strip from the full length of your sheet of paper.
Write the letters A,B,C and D as shown in the diagram.
Draw a line right down the centre of the strip of paper, starting mid-way between A and B and ending mid-way between C and D. Or you can colour each side of the strip in a different colour.
Twist the strip and tape the two ends together so that "A" touches "D" and "B" touches "C." Your strip should now look like this:
If you look at the line that you drew what do you notice? If you coloured the strip, do the same colours match up,? Do you end up back where you started?
The really interesting thing about this strip, are all the things that you can now do with it. For instance, cut your strip down the middle, as though you are cutting two, thinner strips. But do you get two?
How many edges does the new band have? How many sides does it have? How many twists are there in the ring? What have you discovered?
The name of this strip is a Mobius Strip or Band after the mathematician, Alfred Mobius.
This activity features in our
December 2008 Advent Calendar
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Register for our mailing list
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the
Millennium Mathematics Project