chapter  25
4 Pages

Gaussian Co-ordinates

According to Gauss, this combined analytical and geometrical mode of handling the problem can be arrived at in the following way. We imagine a system of arbitrary curves (see Fig. 4) drawn on the surface of the table. These we designate as u-curves, and we indicate each of them by means of a number. The curves u = 1, u = 2 and u = 3 are drawn in the diagram. Between the curves u = 1 and u = 2 we must imagine an infinitely large number to be drawn, all of which correspond to real numbers lying between 1 and 2. We have then a system of u-curves, and this “infinitely dense” system covers the whole surface of the table.