XXV
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 -curves, and we indicate each of them by means of a number. The curves , and are drawn in the diagram.
Fig. 4.Between the curves and 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 -curves, and this ‘‘infinitely dense” system covers the whole surface of the table. These -curves must not intersect each other, and through each point of the surface one and only one curve must pass. Thus a perfectly definite value of belongs to every point on the surface of the marble slab. In like manner we
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