Off-the-shelf Masterclass: Bridges of Konigsberg

Off-the-shelf Primary Mathematics Masterclass about the infamous Bridges of Konigsberg conundrum, first solved by the mathematician Euler.

Explore the properties of basic graphs in this interactive workshop - a great introduction to the mathematics of Graph Theory, the art of reducing complex systems to simple forms.

  • Credit: Alexander Yampolsky via Flickr

About this Masterclass

The city of Königsberg was founded in 1255 in what was then part of Germany, called Prussia. Since 1945 the city is part of Russia and has been renamed Kaliningrad. Historically, the city was laid out across a fork in the River Pregel, with a section of the city on an island in the middle of the river.

People who lived in the city wondered over coffee whether it would be possible to cross all of the city’s bridges in one journey, without crossing any of the bridges twice. Each bridge would be crossed exactly once in some direction. People struggled to find a solution to this problem, and it took a mathematician - Leonhard Euler, who lived in nearby St Petersburg - to find the answer.

This workshop introduces the area of mathematics known as graph theory, and how it was discovered by exploring the historical ‘Bridges of Königsberg’ problem. Students will investigate ways to study graphs in order to categorise them, finishing by redesigning the city of Königsberg to create their own solution.

Examples of graphs in the real world include many train maps such as the London Underground map.

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

Resources needed

  • Bridges of Königsberg Map laminated worksheet (printed A4 or A5) per student, dry wipe marker
  • Path tracing worksheet per student
  • Odd and even vertices worksheet per student
  • Coloured pens or pencils (two colours per student)
  • Euler formula worksheet per student
  • Map of KönigsBLANK per student
  • Computer and data projector
  • Further details of quantities etc. can be found in Session Leader Notes

Support

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. For additional guidance, the session script gives a full run-through of the Masterclass.

The Session Helper Sheet can be distributed amongst helpers and an Additional Information Sheet giving more details on the history and background of the subject is provided for added interest.

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.