Beatrix Schuba was the worlds' greatest skater of school figures. She once traced a perfect circle on the ice. When the judges measured it they found that the radius was exactly one meter and the circumference was c = 6.283185307179560 meters.
What is the radius of the earth?
Hint: For an algebraic solution you will need to know (a) the decimal expansion of π out to 15 decimal places, (b) the formula from spherical geometry for the circumference of a circle of radius r drawn on a sphere of radius R, and (c) the first two terms of the MacLaurin series for the sine function.