# Christoffel Symbol on a Spherical Metric

Classical Mechanics Level 3

$ds^2 = r^2 \, d\theta^2 + \dfrac{1}{1+r^2} \sin^2 (\theta) \, d\phi^2.$

A strange metric on a sphere of radius $$r$$ is given by the invariant interval as described above.

Compute the Christoffel symbol $$\large \Gamma^{\phi}_{\phi \theta}$$.

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