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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

6 votes

Geodesics on the sphere

I always found the following argument the most appealing intuitively. Imagine the sphere is hollow. Obviously the shortest path from $p$ to $q$ is a straight line through the interior of the sphere. …
Vincent's user avatar
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