it's called the euler characteristic. >> euler, the same guy with the bridges of konisberg? >> same guy. very fundamental at the foundations of topology. and the euler characteristic is a number, and we have to get to that number somehow. and the way we get to it is that we break our surface up into little pieces. like in this case we have a torus, or a doughnut, and we've broken it into little quadrilaterals in this picture. >> so it's as if it was constructed by tiles. >> now, once you have those pieces, the count is the following, is that there are things that we are going to call faces, edges, and vertices in that construction. and we can count them. so in this case, we have many, right, if you look at it. now, you can also count the number of edges. >> right, so it's essentially just the lines that i'm seeing here that demarcate where the boundaries are. >> right, you're just counting the lines on that object, and then the vertices are just the points on that object. >> so i've got these three numbers: the number of faces, the number of vertices, and the number of edges