X,Y and Z are three points on a unit sphere (i.e. a sphere with radius 1). The space distance between any pair of the three points is √ 2 (i.e. XY = YZ = ZX = √ 2). An ant can only crawl on the surface of the sphere. The ant starts from point X, passes through points Y and Z, and then returns to X. What is the shortest possible distance of this trip?

Shibu May 23, 2021