For the next critical mass ride, I'm going to try to mount a gong inside the front triangle of my bicycle. Naturally, I want to maximize the radius of the gong and learn some geometry. I spent a couple minutes trying to derive it myself. The number of terms to take care of became huge, so I googled it. http://www.efunda.com/math/areas/CircleInscribeTriangleGen.cfm Looking at the complxity of the final answer, I suppose I did myself a favor by not solving it the entire way for myself. At one point, I had 36 terms and nothing was canceling. My question is, for higher dimentions,(a sphere inscribed in an arbitrary pyramid with triangluar base), does this get mathematically interesting? What about polygons with arbitrary numbers of sides and angles?