Steiner's Minimal Network Problem & Irrational Billiards

Suppose you are a business owner with offices around the country and wish to connect the offices with a private phone network. If the distances involved are large enough, then the cost of setting up the network may be reasonably determined from the total length of wire used alone. This approximation leads to Steiner's minimal network problem. We will discuss various elementary properties of solutions and how considering the problem in different spaces leads to natural geometric questions, including some easy to state open problems involving playing pool on an irrational table. We will cover most of the relevant background material, assuming only very basic trigonometry and calculus. (If you know what sine, cosine, and limits are, then you should be quite comfortable.)