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**[SOLVED] Topology of curved space**

## Homework Statement

The distance between a point (r, theta) and a nearby point (r + dr, theta + d\theta) on a

__positively__curved sphere is given by

[tex]

ds^2 = dr^2 + R^2 \sin ^2 (r/R)d\theta ^2

[/tex]

NOTE: I mean that ds^2 = (ds^2). My question is - how do I use this formula? What is what - can you explain it to me?