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 Trying to be even more exact by Penny)

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 flat surface.  Ordinarily the length of a pencil is from the center of the top to the center of the bottom.  If that is what is 144, then the other (which is a slant height) is √(1+144²)(D-d), to be used in your calculations, rather than 144(D-d).

That's why I consider √(1+144²)≈144.0008680529392 to be more exact than 144.

Posted by Charlie on 2004-02-24 08:21:02