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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