Phil Plait once pointed out that you can calculate the total angular area of the sky this way. If the sky is a sphere with radius 57.3 degrees, then its area is 4*pi*r^2=41,253 square degrees. This makes dimensional analysts SO mad, but you can't argue with results.

Special 10th anniversary edition of WHAT IF?—revised and annotated with brand-new illustrations and answers to important questions you never thought to ask—coming from November 2024. Preorder here!