[SOLVED] Area of curved space 1. The problem statement, all variables and given/known data I have the following metric, which describes a 2D, positive curved space with flat geometry (ie. a sphere): [tex] ds^2\,=\,dr^2\,+\,R^2 \sin ^2 (r/R)d\theta ^2 [/tex] Here ds is the distance between two points (r, theta) and (r + dr, theta + dtheta), R is the radius of the sphere. I want to find the area of the sphere using this metric. 3. The attempt at a solution Using the metric, I have found the circumference of the sphere to be 2*Pi*R (big surprise). Now I want sum up "all the circumferences" on the sphere. Is that possible?