Geography Reference
In-Depth Information
Exercises
1.
Euler's Seven Bridges Problem
Description
Topology is a field of mathematics where distance is not relevant. In this exercise,
you will examine some of the basic concepts of topology.
Exercise Instructions
On this rough map illustrating the seven bridges of Königsberg problem that moti-
vated the mathematician Leonard Euler to develop topology, try to draw with your
pencil in one continuous line a way to walk around the city crossing each bridge
only once.
Questions
Why do you think this is so difficult?
Is it possible?
A second case: assume a flood washes out one of the bridges in Königsberg, leav-
ing six. Draw a route around the city now using one continuous pencil line.
Questions
Does it matter which bridge you take away?
What if you add bridges?
2.
EXTENDED EXERCISE:
Networks, Topologies, and Route
Overview
In this exercise, you will use GPS equipment to determine the locations of several
key points near campus, determine the time to walk between locations, and prepare
a network graph where distance corresponds to time.
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