mgf1107lecture21

# mgf1107lecture21 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 21 The Shortest Network Connecting Three Points In the previous lecture we looked at minimum spanning trees, with the underlying assumption being that we can only select edges from the original network. Now suppose that we want to connect three cities, and minimize the amount of road (or cable) used, with no restrictions as to where the edges can be. Ex. It turns out that this situation is true in general, and that if we are able to create three 120 ° angles in the above manner, then the resulting edges create the shortest network (SN).

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Ex. In 1989 many of the world’s largest telephone companies joined together to pay for a underwater network of fiber-optic cables linking Japan, Hawaii, and Guam (see the map below). Given that the cost of laying the cable was over \$50,000 per mile, it was important to create the shortest possible network. This was done by calculating the Steiner point. Note: Finding a Steiner point is impossible when the three cities form a
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## This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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mgf1107lecture21 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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