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Albert Einstein edited Gaussian Coordinates.tex
almost 11 years ago
Commit id: 1f4cb4995f6e13b87600dc8084771dc71f7f1fae
deletions | additions
diff --git a/Gaussian Coordinates.tex b/Gaussian Coordinates.tex
index 779cdee..5501fac 100644
--- a/Gaussian Coordinates.tex
+++ b/Gaussian Coordinates.tex
...
P': (u + du, v + dv),
$$
where $du$ and $dv$ signify very small numbers. In a similar manner we may indicate the distance (line-interval) between $P$ and $P'$, as measured with a little rod, by means of the very small number ds. Then according to Gauss we have
$$
ds^2 = g_{11} du^2 +2g_{12}\,du \,dv + g_{22} dv^2
$$