algebra problem

Sheldon's version's of the circle problem goes like this. (And this really is how extra-galactic astronomers attempt to measure the curvature of the universe. So far all measurements are consistent with the Euclidean model -- curvature = 0.)

Suppose we could draw a circle of radius 2 meters in empty space, far from any gravitating matter. Suppose that we could measure the circumference so accurately that we could compute pi = C/D out to 52 decimal places. Suppose that the 52nd decimal place of pi computed by this method turned out to be 7 instead of 8.

What is the curvature of the universe?

Hint: c = [2 (textbook pi) / k ] sin (rk). Solve for k as above. (Answer: .07 per billion light years. )

Sheldon told me that.

Click to expand...

Mathman said:

Suppose we could draw a circle of radius 2 meters in empty space, far from any gravitating matter. Suppose that we could measure the circumference so accurately that we could compute pi = C/D out to 52 decimal places. Suppose that the 52nd decimal place of pi computed by this method turned out to be 7 instead of 8. What is the curvature of the universe?

Click to expand...