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Geometry, which is the only science that it hath pleased God hitherto to bestow on mankind ...

In J. R. Newman (ed.), The World of Mathematics, New York: Simon and Schuster, 1956.

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# Leonard Euler's Solution to the Konigsberg Bridge Problem

## Koenigsberg

Editor's Note:  The following student research report was prepared for Professor Judit Kardos' Math 255 class, held at The College of New Jersey. This was a 3 credit introductory course in the History of Mathematics. This report was counted towards 30% of the final grade.  There will soon be a further discussion of the concept and use of student research projects or papers, and further examples.  Look for them soon.

Our story begins in the 18th century, in the quaint town of Königsberg, Prussia on the banks of the Pregel River.  In 1254, Teutonic knights founded the city of Königsberg under the lead of Bohemian King Ottoker II after their second crusade against the Prussians.  In the Middle Ages, Königsberg became a very important city and trading center with its location strategically positioned on the river.  Artwork from the eighteenth century shows Königsberg as a thriving city, where fleets of ships fill the Pregel, and their trade offers a comfortable lifestyle to both the local merchants and their families.  The healthy economy allowed the people of the city to build seven bridges across the river, most of which connected to the island of Kneiphof; their locations can be seen in the accompanying picture.

As the river flowed around Kneiphof, literally meaning pub yard, and another island, it divided the city into four distinct regions.  The seven bridges were called Blacksmith’s bridge, Connecting Bridge, Green Bridge, Merchant’s Bridge, Wooden Bridge, High Bridge, and Honey Bridge.  According to lore, the citizens of Königsberg used to spend Sunday afternoons walking around their beautiful city.  While walking, the people of the city decided to create a game for themselves, their goal being to devise a way in which they could walk around the city, crossing each of the seven bridges only once.  Even though none of the citizens of Königsberg could invent a route that would allow them to cross each of the bridges only once, still they could not prove that it was impossible.  Lucky for them, Königsberg was not too far from St. Petersburg, home of the famous mathematician Leonard Euler