I have a pencil that always rolls around on a slanted surface. One end is wider and heavier than the other. So whenever it rolls, it goes in a wide circle. Otherwise, the pencil is featureless, only becoming steadily wider towards one end.

The difference between the two diameters on the two ends is exactly 144 times smaller than the length of the pencil. If the pencil is pointing uphill on a slanted surface, how many times will it spin until it points downhill?

(In reply to re: Trying to be even more exact by Charlie)

"But this assumes that the 'length' of the pencil is the length of the line where the cylindrical surface of the pencil is tangent to the slanted surface.  Ordinarily the length of a pencil is from the center of the top to the center of the bottom."

Good point!

Posted by Thalamus on 2004-02-24 12:57:25