# Euler and Hamiltonian Circuits

**Topics:**Graph theory, Leonhard Euler, Eulerian path

**Pages:**4 (1379 words)

**Published:**March 24, 2013

As I type this sentence millions of students all over the country are in their math class either a) struggling to open their eyelids or b) tapping their fingers due to boredom and impatience. They have all failed to understand how the topic would later come of use. Although mathematics may seem to be “unnecessary” it teaches our brains to strategize, and think differently through the use of trial and error and problem solving. Most individuals consider mathematics to be a dreadful topic, and can never really comprehend how it can be beneficial in our lives on a daily basis. Most of the time, they may seem to be correct. However, they are not. Most of the time, we are using its strategies without even acknowledging it. We use it for almost anything we do: currency, measurement, time, etc. Two examples of math we use on a regular basis are Euler and Hamiltonian Circuits. An Euler Circuit is a circuit that reaches each edge of a graph exactly once. (Malkevitch, 8) This theory is named after Leonhard Euler, an outstanding mathematician during the 18th century. Euler had been the first person to study this category of circuits. In addition, he was the creator of the theory of graphs, or graph theory. One of the many things he had found was that most graphs do not have an Euler circuit at all. Euler had also contributed to the field of mathematics in various ways. He was a very creative individual, establishing more than 500 works throughout his lifetime. Euler had been considered a prodigy because he was working with the most complex mathematical calculations under the very poor conditions he lived in, and proceeded to work with these problems until he had become totally blind. (Malkevitch, 9) According to Professor Clark Kimberling, some of the other things Euler had discovered or had named after him in his honor are: e (the calculus number), a,b,c (the side lengths of a triangle), f(x) (for functional value), R and r (the circumradius...

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