Ok, so this relates to my homework, but I really can't find an answer anywhere, so this is more of a general question. First off, what does a "chart" of a manifold look like? Is it a set, a function, a drawing, a table, what?! I have found so many things about charts, but nothing shows what they actually look like (either that or I am just not recognizing them). Secondly, using stereographical projection, what are the 4 charts of a torus? I saw something that looked something like x1 = ((cosΘ, sinΘ), (cosφ, sinφ))= Θ x2 = ((cosΘ, sinΘ), (cosφ, sinφ))= φ and the other charts are similar. Would the other charts just be y1 = ((cosΘ, sinΘ), (cosφ, sinφ))= Θ y2 = ((cosΘ, sinΘ), (cosφ, sinφ))= φ I'm just really confused on this topic and I would like to gain a little more confidence before going into my final. Are the "charts" that I gave actually charts, and are they the ones that describe a torus?