Consider points X,Y, Z on a unit sphere. The space distance between any of these pairs of points is \(\sqrt{2}\). An ant can only crawl on the surface of the sphere. The ant starts at point X, and passes through Y and Z, then returns to X. What is the shortest possible distance of this trip.

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My work: I know that the shortest possible distance between two points on a sphere is the great circle. Since XY=YZ=XZ, the shortest distance will simply be the circumference of a circle with radius 1. which is 2pi. Is this correct, or do I have a flaw in my logic? Thanks in advance. :)

Guest Jun 2, 2021