Seven Bridges of Königsberg

By Math Is Fun, December 26, 2023

“Have you ever heard of the Seven Bridges of Königsberg?” I asked my son. He leaned in, curious.

“In an old city named Königsberg, there were two islands in a river, connected to each other and the mainland by seven bridges. The townspeople had a puzzle: could you walk around the city and cross each bridge exactly once?”

My son looked thoughtful. “Can you really do that?”

“That was the big question,” I said. “Everyone tried, but no one succeeded. Then came Euler, a brilliant mathematician. He approached the problem differently. It wasn’t about the walking or the city’s layout, but about how the land areas were connected.”

To help him visualize, I sketched a simple diagram. “Think of each land area as a point and each bridge as a line. Euler found that to make such a walk possible, all but the start and end points must connect an even number of bridges (going in and out since you can cross each bridge only once). However, in Königsberg, every single area was connected by an odd number.”

“So, it couldn’t be done,” my son realized.

“Precisely,” I confirmed. “Euler proved its impossibility. His work on this puzzle laid the foundation for a whole new branch of mathematics called Graph Theory. He was only 29 at the time.”

Euler is recognized as one of history’s most eminent mathematicians and the most distinguished of the 18th century. He’s renowned for introducing the use of the Greek letter \pi (lowercase pi) to represent the ratio of a circle’s circumference to its diameter. Additionally, Euler was the first to employ the notation f(x) we use today for the value of a function, among his numerous other contributions.

My son pondered the sketch. “So some puzzles show us that there’s no solution?”

“Indeed,” I nodded. “Euler’s genius was in seeing problems from new angles. He taught us the importance of rethinking our approach to find answers, or in some cases, to understand why answers don’t exist.”

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