Mathematicians required

Posted by y on Apr 16, 2002 at 07:59
(194.205.118.26)

Problem: to connect 9 circles arranged in a square, with 1 straight line, without folding or tearing the paper.

Possible solution:
1) take a piece of A4 paper, cut a lengthwise strip about 1 inch in width.
2) draw the 9 circles on it in the shape of a Rhombus.
3) Twist the paper through 180 degrees
4) take 2 small pieces of sticky tape,
5) join the 2 ends of the paper together (using 1 piece of tape for 1 edge and 1 piece of tape for the other edge, leaving a gap where the paper is not covered by tape.
6) you now should have a Mobius strip/band.
7) take your pen and connect the first 3 circles (lengthwise along the strip, going with the angle of the Rhombus).
8) continue around the strip/band until you have connected all of the circles.

Points of discussion, (bearing in mind that the strip/band has only 1 edge and 1 side).

1) is there a fold in the paper? To me this is not a fold, but a curve. (does anybody out there disagree with this distinction)

2) is the line a spiral? (in a mathematical sense)

3) is the line straight ( in a mathematical sense)

4) is it something else

5) does the use of the Rhombus make any difference whatsoever (to the possible validity of this possible solution).

Somebody out there must know the answers to the above questions, (they are probably quite obvious answers), so please prove me right, or wrong, as the case may be.