¶ Euler (2)
Index Entry
Euler:
"He was finally able to say that on a plane pattern the number of the vertexes plus the number of the areas will always equal the number of the edges plus the number one. Looking at a polyhedron and thinking about it as a flat picture, we can count these up. The number of vertexes is 18, and the number of faces is 19, so 18 + 19 = 37, but the number of edges is 36 and the plus one makes 37. Euler found that he could do this for structures which were not in the plane. And then the accounting becomes the edges plus two instead of the edges plus one.
"If the pattern has a hole through it, like a doughnut, then we don’t have plus anything. We leave out the two from the solid. When we leave out the two from the solid it is really a doughnut, and we are cutting out the axis which is to say that the axis is two.
“In other words when I say frequency to the second power times ten plus two, I assign two in every layer for the axis. We must pay attention to the fact that the ‘plus Two’ that Euler found has to be added to the vertexes plus faces equals edges plus two, when it is a structure in the round; but when we”
