History of mathematics · Maths EE idea · Accessible
From Königsberg to graph theory
A research question to start from
How did Euler's solution to the Königsberg bridges problem lay the foundations of graph theory, and how does a modern proof differ from his argument?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Comparing an original argument with a modern proof shows how mathematical rigour changed.
Mathematics you would need
- Graphs and degree
- Eulerian paths
- Proof structure
- Generalisation
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Summarise Euler's argument in your own words.
- Give a modern proof of the theorem.
- Compare what each proves.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- Retelling the story.
- No modern proof.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Euler Konigsberg original argument; Eulerian path theorem modern proof. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).