Leonhard Euler

Leonhard Euler was born in Switzerland on April 15th, 1707. Euler studied many areas of mathematics including calculus, trigonometry, geometry, algebra, and number theory. He is one of the most prolific mathematicians of all time. He published 886 papers and books.

In 1736 at age 29, Euler solved a very interesting problem. Mathematicians know this problem as the “Seven Bridges of Konigsberg.” The problem is stated as follows: In the city of Konigsberg in Russia, there are 7 bridges. These bridges help connect the city that has been separated by rivers. Is it possible start walking from one part of Konigsberg and cross each bridge exactly once and return to your starting point?

graph 1

Euler was able to show that it is impossible to construct such a path. He did so by viewing the problem in a more abstract, but simpler way. This is how Euler visualized the problem.

graph 2

He removed all of the unnecessary detail and represented the landmasses as dots and the bridges as lines. He called the blue dots “vertices” and the black lines “edges.” By doing so, he invented an entirely new branch of mathematics called graph theory.

Your task is to solve the same type of problem as Euler. Below are some different “graphs.” Either show a way to start at one vertex, use every edge exactly once, and arrive back at the same vertex, or explain why this is impossible.

graph 3

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