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?

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.