MathDB

A right circular cone has base radius

r

and height

h

. The cone lies on its side on a flat table. As the cone rolls on the surface of the table without slipping, the point where the cone's base meets the table traces a circular arc centered at the point where the vertex touches the table. The cone first returns to its original position on the table after making

17

complete rotations. The value of

h/r

can be written in the form

m\sqrt {n}

, where

m

and

n

are positive integers and

n

is not divisible by the square of any prime. Find m \plus{} n.

Problem Statement