Dec 6 - Berggren's Episodes in the Mathematics of Medieval Islam

I was amazed how Al-Biruni "discovered two new map projections, one known today as the azimuthal equidistant projection and the other as the globular projection." It would be great to get my students a bunch of different map projections and see that there is no perfect 2D map projection of a sphere. It could also be a good introduction to geodesics and make them answer the question of "what is the shortest path a plane can travel on the Earth?".

I wasn't aware that Umar al-Khayyami "systematically studied all the kinds of cubic equations and used conic sections to construct the roots of these equations as line segments obtained from the intersections of these curves." I could easily get my students to do this, and see what solutions they get. Another one would be how he thought that square root of two and "pi" should be a different kind of number. It would be awesome if students find these numbers by themselves and realize or prove that they can't be rational numbers.

I didn't know that Al-Kashi had a treatise on an "instrument known as an equatorium. This instrument is, in essence, an analog computer for finding the position of the planets according to the geometrical models in Ptolemy’s Almagest, and its utility is that it allows one to avoid elaborate computations by manipulating a physical model of Ptolemy’s theories to find the positions of the planets.". I would buy or make one and get the students to experiment with it, and then find the actual dimensions by researching the internet (or using Stellarium) and see how accurate his instrument was.