Flexagons and Catalan numbers
Catalan numbers are one of my favourite types of numbers! They pop up regularly in situations where things need to be counted (a branch of mathematics called combinatorics). Catalan numbers …
Course: Flexagons and the Math Behind Twisted Paper
Les Pook’s Flexagon Symbols
Les Pook has written two classic books on flexagon theory. His second book, Serious Fun with Flexagons, is a rigorous, comprehensive analysis of many kinds of flexagons, the nets from …
Möbius Strips and knots
Take a strip of paper, make 3 half-twists in it and join the ends to get a 3 half-twisted Möbius band. Now, cut this 3-strip in half. The result is …
Cyclic flexagons are Möbius strips!
At first glance, it looks like flexagons and Möbius strips are exact opposites. Möbius strips have one or two sides, depending on the parity of the number of half twists. …
Möbius Strip summary
You have watched and played with Möbius strips. Let’s summarise what we’ve learnt. Odd and even half-twisted paper strips A strip of paper has two sides. Attaching its ends together …
The Möbius Strip and its variants
In this step, we’re going to take a look at some Möbius strips. I can’t emphasise enough, how important Möbius strips are to mathematics, so it is really important to …
Farewell
So! We have reached the end of the course. We do plan on offering more courses like this on FutureLearn so please, do stay tuned. The Weizmann Institute of Science …
The tetra-octa-flexagon
Watch the video and follow the instructions to build the tetra-octa-flexagon: Download the file below which has the templates for the back and front of the paper strip that will …
The hexa-hexa-flexagon
Watch the video and follow the instructions to build the hexa-hexa-flexagon: Download the file below which has the templates for the back and front of the paper strip that will …
Introduction
This week we’re going to take a look at advanced flexagons and we’ll start with two important flexagons, the straight-strip, cyclic, hexa-hexa-flexagon (6-6-flexagon), and the straight-strip, cyclic, tetra-octa-flexagon (4-8-flexagon). Notice …
The magic square flexagon
Watch the video and follow the instructions to build Robin Moseley’s magic square flexagon. This flexagon features four famous magic squares created by Josep Maria Subirachs (the Sagrada family church …
Magic squares
Magic squares have fascinated mankind for thousands of years. No one really knows the origin of magic squares, but many historians think that they were invented in ancient China. What …
Tuckerman Diagrams
The previous article may have left you confused, so let’s recap what we know about flexagons and be specific as to how we are going to refer to them for …
Flexagon analysis
Let’s return to the basic tri-hexa-flexagon and explore some of its properties. You made this flexagon from a pre-coloured strip of paper. Of course, Arthur Stone and his friends didn’t …
The non-cyclic hexa-tetra-flexagon
Watch the video and follow the instructions to build the non-cyclic hexa-tetra-flexagon: Download the file below which has the templates for the back and front of a rectangular sheet of …
