Math Problem - Seven Bridges
Posted by David Wetzel
Problem Solving Strategies
The foundations of topology are often not part of high school math curricula, and thus for many it sounds strange and intimidating.
However, there are some readily graspable ideas at the base of topology that are interesting, fun, and highly applicable to all sorts of situations.
One of these areas is the topology of networks, first developed by Leonhard Euler in 1735. His work in this field was inspired by the following problem.
Seven Bridges Problem
In Konigsberg, Germany, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts.
Seven bridges were built so that the people of the city could get from one part to another.
The people wondered whether or not someone could walk around the city in a way that would involve crossing each bridge exactly once.
The following is drawing of the seven bridges in Konigsburg, Germany:
Sketch the above map of the city on a sheet of paper and try to ‘plan your journey’ with a pencil in such a way that you trace over each bridge once and only once and you complete the ‘plan’ with one continuous pencil stroke.
The problem now becomes one of drawing this picture without retracing any line and without picking your pencil up off the paper.
Leonhard Euler
A Swiss mathematician (1707 -1783) who made enormous contributions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory.
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