Tuesday, April 07, 2015

For The Math Lovers Out There

The city of Koenigsburg, which spanned two sides of a river as well as an island in the river and land at the fork of the river, was connected by 7 bridges.  The locals used to try to cross each bridge exactly once and return to where they started.  This was the Koenigsburg Bridge Problem, and over 2 centuries ago Leonhard Euler, one of the best mathematicians of all time, showed why it couldn't be done and what bridges would have to be built in order for it to be able to be done. 

I guess those Wall Street writers at Business Insider think about more than just money:
Business Insider is headquartered in a city that also has a number of bridges, and so we were curious as to whether a tour of the bridges of New York City, going over each bridge exactly once, was possible.
Why does anyone care?
This particular puzzle is, at a glance, mostly just a fun observation, whose only application is for particularly fastidious marathon runners. However, it holds an important place in the history of mathematics. Euler's writings on the Bridges of Koenigsburg problem represented some of the first work in what would become the modern mathematical areas of topology and graph theory...

Graph theory is enormously useful in studying networks. Power grids, computer networks, and relationships between people on social networking sites — to give just a few examples — can all be modeled by different types of graphs, and results from graph theory are essential to understanding and managing these complex systems.
So yeah, pretty cool stuff.


PeggyU said...

You taking a topology class?

Darren said...

Last semester I took a discrete optimization class, which included some graph theory.