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Albert Einstein edited Gaussian Coordinates.tex
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\section{Gaussian Coordinates}
Two neighbouring points $P$ and $P'$ on the surface then correspond to the co-ordinates
where $du$ and $dv$ signify very small numbers. In a similar manner we may indicate the distance (line-interval) 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 co-ordinates are simply Cartesian ones.