Chapter 5: The Mathematics of Getting Around

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Presentation transcript:

Chapter 5: The Mathematics of Getting Around

Seven Bridges of Königsberg Is it possible to take a walk that crosses every bridge exactly once?

Seven Bridges of Königsberg

Seven Bridges of Königsberg What about for a city with any number of islands and any number of bridges? http://en.wikipedia.org/wiki/Leonhard_Euler

Sunnyside A security guard parks his car at S. Is it possible for him to patrol every street exactly once (and end back at his car)? If not, what is the best he can do?

Sunnyside The mailman begins and ends at P. What is the optimal mail delivery route? (Streets with houses on both sides must be walked twice.)

Unicursal Tracings Is it possible to trace each figure without lifting your pencil or retracing any lines?

Routing problems A routing problem is any problem that deals with trying to find ways to route the delivery of goods or services to destinations. What are some examples of routing problems? The examples on the previous slides are a specific kind of routing problem called Euler circuit problems – in these problems, we are trying to find a route that covers every bridge/street/line only once.

Routing problems In any routing problem, we would like to find an optimal solution. Depending on the situation, optimal can mean: Cheapest Fastest Shortest distance Some other measurement The goal is to find the most efficient way to solve the problem. The area of math that deals with these sorts of problems is graph theory.