>That is right, the entire space is curved. Especially for large circles (or close to large masses), the relationship between circumference and diameter might be way off the theoretical value of pi.
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>It was at one time believed that space was "flat" (Euclidian), but nowadays we know that this is not true.

Or that the truth depends on the distance, i.e. for circles small enough, the Pi is good enough. Actually, Pi can be defined as the final value of the ratio of circumference and diameter as the curvature of space approaches zero.

The funny thing is that you can explain curved space by comparing the flat planar geometry with the geometry on a sphere... and then at some point you have to confess that the curvature of our space is actually negative. Confuses the hell out of everyone :).