A Knotty Pentagram

The five diagonals of a regular pentagon define a star-shaped figure known as a pentagram. For millennia, the pentagram has been associated with mystery and magic. In ancient Greece, the Pythagoreans referred to it as a pentalpha because it consists of five alphas (A). The geometric proportions of a pentagram are those of the golden section. Any two line segments that share an endpoint will be adjacent sides of a golden triangle, either (36°-72°-72°) or (36°-36°-108°).
You can make a pentagram by tying a knot in a strip of paper. Begin with a strip of wax paper, a foot long and an inch wide (30 cm x 2.5 cm). Tie an overhand knot like the first knot in tying a shoe lace (below left). Carefully tighten the knot, creasing the folds so all of the edges meet and it lies perfectly flat (below center). Fold the right end of the strip to the rear and crease it along the right edge of the regular pentagon. If you look through the translucent pentagon, a pentagram will be revealed (below right). If you wish, trim the surplus lengths of the strip flush with the edges of the pentagon.

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