Spider and Fly

On a plane the shortest distance between two points is a straight line. Suppose a spider sits on a cube and wants to catch a fly sitting on the opposite face. How would you determine the path of shortest distance for the spider to crawl on the surface to catch the fly?

Answer

To find the shortest path between any two points on a cube not on the same face, one convenient method is to lay out the six faces of the cube on a plane

and draw the straight-line path. Of course, all parts of the path must be on the faces, and the appropriate faces sharing a common edge must retain their relative positions and orientations.

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