Euler and Hamiltonian Circuits

1379 WordsMar 24, 20136 Pages
Euler and Hamiltonian Circuits 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…show more content…
Euler Circuits prohibits the reuse of edges whereas Hamiltonian Circuits do not allow the reuse of vertices. Both Euler and Hamiltonian circuits are extremely beneficial in our daily lives because they are classified under problems known as “routing problems”. According to Professor Larry Bowen, “routing problems” are problems whose solution attempts the most efficient way(s) of routing things among different destinations. These problems may appear in various areas such as: transportation, communications, and the delivery of services. Without our realization, we use Euler problems on a day-to-day basis specifically in management science. Anytime it is necessary for services to go through streets or roads the Euler Circuit theory can be more resourceful. To show more specific problems, Euler circuits can help an individual while they are salting icy roads, plowing snow, mowing grass along highways, collecting garbage, collecting debris or leaves from urban curbs, inspecting railroad tracks for flaws, or reading electric meters at private houses. (Malkevitch, 19) We use them to indicate where the arrows on the streets should be placed, and in what direction they should go in. In addition, we use them to construct the schedules for when parking is forbidden. Because parking-times are massive factors in street sweeping, it is essential find a circuit that visits streets when they are free of cars. Also, we

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