Off-the-shelf Masterclass: Mobius band

Play with simple strips of paper for this fun mathematical activity that will blow the minds of both the young students and attending adults alike. Wow them with this lovely introduction to the mathematical field of topology.

children playing on a playground that is shaped like a mobius band
Image credit: Biswarup Ganguly via Wikimedia Commons

About this Masterclass

The Möbius Band, discovered in 1858 by August Möbius, is a special shape that only has one face and only one outside edge. It is therefore an example of what is known as a non-orientable surface. 

The interesting behaviour of the Möbius Band observed in this workshop is caused by these two properties - having only one face and one side means you can draw a line between any two points on the band without crossing over the edge. Going against everyone’s intuition, it will not split into two pieces when cut in half length-ways.

It is very easy and fun to make Mobius bands out of strips of paper, and then explore and dissect them to investigate their extraordinary mathematical properties.

Length: 2 hours (see the session leader notes for ideas on how to shorten the Masterclass).

Resources needed

  • ‘Mobius Band’ presentation (download from "Supporting documents" below)
  • Student worksheet, 1 per student (download from below)
  • Supporting notes; helper/ session leader (download from "Supporting documents" below)
  • A4 blank or brightly coloured paper (one sheet per student, with some spares in case)
  • Pre-cut strips of paper in two colours
  • Scissors, glue/tape, pencils and rulers for each student - glue/tape may be shared, but for everything else one each will be needed
  • Möbius properties worksheet (one per student)
  • Internet access to some YouTube videos (linked to in the presentation)
  • Computer and data projector
  • Further details of quantities etc. can be found in Session Leader Notes

Worksheets

01 Mobius Bands Worksheet

Solutions

Mobius Band worksheet solutions

Supporting documents

Session leader notes Helper notes Additional information Session script Mobius Band Presentation

Support for this Masterclass

All supporting notes, worksheets and solutions can be downloaded from this page along with the Powerpoint presentation.

The Session Leader Notes offer full notes on the activities and a detailed list of resources, including quantities needed. 

The Session Helper Sheet can be distributed amongst helpers so they can better support the students.

Ask the Ri

You can collect any student questions and email them to the Ri Masterclass team at masterclasses@ri.ac.uk - we will endeavour to answer them before the next Masterclass in your series.

Masterclass series support

For more information on running a Masterclass series and the support, templates and other resources available to you, please get in touch via masterclasses@ri.ac.uk.

Back to top