Off-the-shelf Masterclass: Bridges of Konigsberg

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