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Chapter 5: The Mathematics of Getting Around

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 ?

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Chapter 5: The Mathematics of Getting Around

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  1. Chapter 5: The Mathematics of Getting Around

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

  3. Seven Bridges of Königsberg

  4. 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

  5. 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?

  6. 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.)

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

  8. 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.

  9. 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.

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