I have a strip of paper with parallel sides, a pencil and a straight edge. How can I construct a regular pentagram (star) with these? And for that matter, a pentagon? Well ... the pentagon is the proper way to go.

(In reply to re: A trick by SilverKnight)

Re SK's Q about the L:W ratio of the strip. I started off with a strip of paper and performed Brian's trick to produce a pentagon. Trimming off the excess from each end and undoing the knot shows that the piece of paper is a parallelogram.

Assume the pentagon has vertices ABCDE, then the length of the long sides of the parallelogram is equal to 2AB + 2AC. This means that the length of the paper is equal to 2AB + 2 AC plus a little bit.

I assumed that the final pentagon had sides of unit length, which meant that the piece of paper had dimensions:

width = sin72 = 0.9511
length = 4sin54 + 2 + cos72 = 5.5451

which gives a ratio L:W of 5.8304 : 1

Posted by fwaff on 2003-09-22 11:59:24