Nov 11, 2009

Globe Traversal Problem

how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you're walking on a static sphere if that makes the problem less complicated to you.

1 comment:

  1. infnity.one point is the northpole. the rest of em are near the south pole. for example, take a circle of circumference one mile with its centre as the southpole. Now make a bgger circle with radius equal to the radius of the previous circle plus 1. so every point on this new circle satisfies the given ciinditions. take a point, walk one mile south, u reach the inner crcle. walk one mile west, u cover one circle and reach back to the same spot and walk one mile north from there, u have come back to the starting point.. u can repeat this taking inner circle of circumference 0.5 miles, 0.25 miles and so on...

    ReplyDelete