Post by Peter
Greetings from Holland!
My new puzzle is inspired by a pencil rolling over my desk. It seems
not to be too difficult, thereforeI would be delighted to receive an
email with your solution.
Have fun with the puzzle (to be found at
www.planet.nl/~p.j.hendriks/ppvdw.htm ) !!!
You're asking how far one vertex of the hexagonal cross section of your
pencil travels when the pencil makes one complete revolution while rolling
across the desk. I defined six arcs from one vertex of the hexagon to the
next until the given vertex returned to its original position relative to
the others. In the diagram on your website, "A" would go through each of the
six possible positions and return to its original position as the left-hand
terminus of the bottom side.
For an arbitrary side of length s, I get:
( PI * s * ( 4 + (3 ^ .5))) / 3
When s = 0.5 cm, as in your example, this would be 3.001 cm.
Am I at least close to the correct answer?