Relativity: The Special and General Theory by Albert Einstein is part of HackerNoon’s Book Blog Post series. - science physics
where du and dv signify very small numbers. In a similar manner we may indicate the distance between P and P′, as measured with a little rod, by means of the very small number ds. Then according to Gauss we have
Under these conditions, the u-curves and v-curves are straight lines in the sense of Euclidean geometry, and they are perpendicular to each other. Here the Gaussian coordinates are simply Cartesian ones. It is clear that Gauss co-ordinates are nothing more than an association of two sets of numbers with the points of the surface considered, of such a nature that numerical values differing very slightly from each other are associated with neighbouring points “in space.
We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which “size-relations” are defined. To every point of a continuum are assigned as many numbers as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers which differ by an indefinitely small amount are assigned to adjacent points.
About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Einstein, Albert, 2004. Relativity: The Special and General Theory. Urbana, Illinois: Project Gutenberg. Retrieved May 2022 fromThis eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org, located at https://www.gutenberg.org/policy/license.html.
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