1. Introduction: You must state and define how to measure the center of Utah. You must also talk about why this question is interesting, why this question is difficult, and what other answers you might find on the internet.
2. The mathematics involved: Give a detailed explanation of the mathematics involved in finding the center of Utah.
3. The calculation: Explain your calculation, give the answer.
4. Conclusion: Interpret your result. What does it mean? Please show a visual representation of your answer. You must also mention how the accuracy of your calculation could be improved if you were to redo this project.
Your group must give a brief in­class presentation. The presentation should be based on your paper, and it should be between 10 and 15 minutes long. Please make your presentation visually appealing.

ESSAY GOES HERE Our group decided to measure the center of Utah by finding the center of mass. Certain internet folks have decided on other methods, such as interpreting the town of Levan as
“navel” backwards and considering it the center (no, really). We treated Utah as a uniform, two dimensional object on the surface of a three dimensional sphere. In other words, Utah was for our purposes a flat object occupying three dimensional space. Finding the center of mass of this involves some relatively tricky mathematics, as three dimensions are much more complex to operate with than 2. Our goal was ultimately to discover a latitude coordinate, a longitude coordinate, and a distance from the Earth’s center. Because for our purposes Utah is a curved shape, the center of mass is not actually located on the state itself. It is instead found some distance beneath it, outside of its boundaries.

The mathematics themselves were quite complex. Making use of iterated integrals and multivariable calculus, we attempted to locate the center of mass along the east­west axis and north­south axis. To do this we had to account for the Earth’s radius and the angles along both a vertical and horizontal axis. In our equations, these constituted the Greek letters P, Φ, and Θ. The math is below:

Our original result pegged the center of Utah somewhere off the coast of northwest Russia.
This seemed somewhat inaccurate. However, this was a result of a relatively simple