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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
2
votes
Riemann's formula for the metric in a normal neighborhood
There is the following way of doing it. Let $\Gamma_{ijk}\equiv g_{is}\Gamma^{s}_{jk}$. Then (see here)
$$
g_{jk}(x)=\delta_{jk}+\int_0^1 \alpha ~x^i\Gamma_{[ji]k}(\alpha x)~d\alpha
$$
If we expand $\ …