MECHANICS AND THE THEORY OF RELATIVITY by hans jacobs

Author:hans jacobs [jacobs, hans]
Language: eng
Format: epub
Published: 2020-11-13T00:00:00+00:00

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twenty euclidean geometry. The reader will notice that the situation described here is corresponds with that which has brought with it the postulate of general relativity (section 23).

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§25. Gaussian coordinates

This geometrical-analytic treatment can be obtained, according to Gauss, from the Following way. Imagine drawn on the tabletop a system of arbitrary curves (see Fig. 3), which we call u curves and each of which we characterize with a number. In the figure the curves u = 1, u = 2 are drawn

and u = 3. But between the curves u = I and u = 2 you have to imagine drawn infinite plus, corresponding to all real numbers that are between 1 and two.

We then have a system of curves u that cover the table in a way infinitely dense. No curve u cuts to any other, but for each point of the table passes a curve and only one. At each point on the surface of the table then a perfectly determined u value corresponds . Suppose also that a system of curves v has been drawn on the surface that satisfy the same conditions, which are similarly characterized by numbers and which can also have an arbitrary shape.

Figure 4

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