The hardest midterm I ever took was a Numerical Analysis take-home exam. One problem asked for a definition of "the circle that best approximates four co-planar points" and apply our definition to given data. This problem has clear applications to transceiver placement optimization; e.g., where to put a cell phone tower. The model discussed in this preprint describes not only multiple transciever locations, but also the cost to power a signal within a given radius from each tower. It's rare and wonderful to see a real world problem that translates so naturally to a mathematical model.

The professor for the above mentioned Numerical Analysis course, L. Pachter, has some geometric concerns of his own. In this case, the translation from real world problem to mathematical model is considerably harder to understand, mostly because the geometry does not take place in a plane or 3-space. The fundamental object is still a convex body, but it now lives in a larger number of dimensions. Don't let this scare you off; such models are extremely effective for countless applications.

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