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challenging question?
Mount Mathematica is a cone with top angle alpha. The surface is smooth and therefore frictionless. If we throw a lasso (with a fixed non-sliding knot) over the top of the cone and pull ourselves up parallel to the mount's surface, the lasso stays over the top if the angle is not too blunt. So, what is the maximum top angle that allows us to climb up?
The answer is 60 degrees for the top angle. There is a very neat way of solving this when you take a pla(i)ne view...
