The geometry on the surface of a sphere is noneuclidean, so the circumference \(C\) and radius \(R\) of a circle drawn on the sphere do not obey \(C=2 \pi R\), where for example the circumference is a constant-latitude path and the radius is drawn on the sphere down from the north pole along a constant-longitude path. Suppose we measure latitude by the angle, measured from the center of the sphere, between the north pole and constantlatitude path.

(a) If the angle is \(90^{\circ}\), what is the coefficient \(\alpha\) in \(C=\alpha R\) ?

(b) If in effect \(p i\) were 3.00000 instead of 3.14156 . What would be the angle in that case?

(c) The feature that \(C<2 \pi R\) is a property of a positively curved surface. In Euclidean geometry, given a line and a point exterior to the line, there is one and only one line through the given point that is parallel to the given line, parallel meaning that the two lines never meet. What is the analog statement for a positively curved surface?