# math 1025: exploring mathematics in the everyday world

## Discussion: Where Do I Know You From?

Imagine using math to explain how you know your friends and acquaintances. Were any of the people in your life introduced to you through another friend or acquaintance?

In this Discussion, you will create a visual representation that models relationships similar to the “six degrees of separation” as presented in your readings.

To prepare for this Discussion:

• Select a favorite television series, movie, or novel with an extensive cast of characters that you consider interesting. Determine a relationship that exists among some, but not all, of the characters.
##### Initial Post: By Day 3

Consider the following graph, which represents the one-way airfare between five cities.

A       B               C              D                  E

A *    \$220            \$240          \$290              \$430

B \$220       *                 \$260          \$320              \$360

C \$240   \$260                 *          \$180              \$300

D \$290   \$320            \$180               *              \$250

E \$430   \$360            \$300          \$250                   *

A. First use a graph tool like Graph Creator to represent the information in the table. Use vertices to represent the cities and weights on appropriate edges to show the airfares. Here is the website https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Graph-Creator/

B. Next, assume that you are a salesman who lives in one of the cities (pick any city except for A) and required to fly to all for of the other cities and return to your home city. Describe how you would use the Nearest Neighbor Method to determine the optimal route. What is the total cost for this Hamilton circuit?

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