Re: [math-fun] Gary Antonick is edging away from the following bonus puzzle

Gene, is there a rigorous proof of that using just Eucidean solid geometry, without calculus? --Dan ----- That z is uniform in [-1,+1] is a consequence of the solid geometry theorem that the area of a sphere between two parallel planes depends only on the separation between the planes, and is independent of what part of the sphere lies between the planes. -----