You have a block of wood 1 by 2 by 7 units. One of the 2 by 7 faces has 2 nails inserted, the heads and part of the shaft of each nail protruding. If the coordinates of the corners of this face are: (0,0), (0,2), (7,2), and (7,0), then the nails are located at (1,1) and (6,1).

Assume the coefficient of friction between string and wood is zero, and that the diameter of the nails is negligible.

(1) The ends of a non-elastic string of length 13 units are attached, one end to each of the 2 nails. The string is taut. How is this possible?

(2) What about a second piece of taut string, approximately 8.544 units long, also with ends attached to the 2 nails?

(3) What about a third piece of string approximately 22.0880 units long?

Part 2.  8.544 is close enough to sqrt(73) to use it as such.

And 73 = 64 + 9 =  8^2 + 3^2.

Start at one nail and go in the opposite direction from the other nail. Pass around the end to the back then use one of the sides to transit back to the front to the second nail.  This gives 3 units to transverse the block and 8 units to wrap around the end and return to the other nail.

Hmmm the last part. . .

Posted by Leming on 2005-08-08 15:41:58