Subscribe to Make Magazine Today!

By George Hart for the Museum of Mathematics

Math_Monday_banner02_600px.jpg

If you take a long strip of paper, tie a simple overhand knot in it, tighten it up, and press it flat, the result is a regular pentagon.

knot strip Math Monday: Paper knot pentagons knot star Math Monday: Paper knot pentagons

That construction is well known, and can be found, for example, in Martin Gardner’s Second Book of Mathematical Puzzles and Diversions, where it is also pointed out that if you add one more fold and hold the paper up to the light, a pentagram shows through. Try it!

knot sphere Math Monday: Paper knot pentagons

A newer idea I haven’t seen before is to continue knotting the strip into complex spherical patterns. Heinz Strobl designed this paper sphere made of 120 knots. It has twelve star-shaped openings and twenty openings that are nine-sided. This model is made by Rosa Sanchez. Instructions to make your own are given by Paula Versnick here.

More:
See all of George’s Math Monday columns

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor for Boing Boing and WINK Books. And he has a new best-of writing collection and “lazy man’s memoir,” called Borg Like Me.


Related
blog comments powered by Disqus

Related Supplies at Maker Shed

Follow

Get every new post delivered to your Inbox.

Join 29,166 other followers