Table of Contents:
The Bridges of Konigsberg
The Value of Pi
Prime Numbers
Famous Paradoxes
The Problem of Points Proof of the Pythagorean Theorem

Topology is one of the newest branches of mathematics. A simple way to describe topology is as a
'rubber sheet geometry'  topologists study those properties of shapes that remain the same when
the shapes are stretched or compressed. The 'Euler number' of a 'network' like the ones presented later
in this discussion is an example of a property that does not change when the network is stretched or
compressed. 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:
In Konigsberg (modernday Kaliningrad, Russia), 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. A
crude map of the center of Konigsberg might look like this:
Problem 1
Problem 2
Problem 3
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