Making a Paper Knot to show the Golden Section in a Pentagon

Here's an easy method to show the golden section by making a Knotty Pentagram; it doesn't need a ruler and it doesn't involve any maths either!

Take a length of paper from a roll - for instance the type that supermarkets use to print out your bill - or cut off a strip of paper a couple of centimetres wide from the long side of a piece of paper. If you tie a knot in the strip and put a strong light behind it, you will see a pentagram with all lines divided in golden ratios.

┬ęThis is my favourite method since it involves a Knot(t)!

Here are 5 pictures to help (well it is a pentagram so I had to make 5 pictures!) - although it really is easy once you practice tying the knot!

1. As you would tie a knot in a piece of string ...

2. ... gently make an over-and-under knot, rolling the paper round as in the diagram.

3. (This is the slightly tricky bit!)

Gently pull the paper so that it tightens and you can crease the folds as shown to make it lie perfectly flat.

4. Now if you hold it up to a bright light, you'll notice you almost have the pentagram shape - one more fold reveals it ...

5. Fold the end you pushed through the knot back (creasing it along the edge of the pentagon) so that the two ends of the paper almost meet. The knot will then hang like a medal at the end of a ribbon. Looking through the knot held very close of a desk-light or table lamp will show a perfect pentagram, just like the (red) diagram above.

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