# Blog

## Archive

Show me a random blog post**2019**

### Jun 2019

Proving a conjecture### Apr 2019

Harriss and other spirals### Mar 2019

realhats### Jan 2019

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**2012**

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accuracy propositional calculus christmas martin gardner javascript go fractals map projections royal baby graph theory raspberry pi sorting twitter mathslogicbot manchester palindromes ternary coins flexagons polynomials asteroids data pizza cutting python logic a gamut of games rugby error bars sport electromagnetic field radio 4 cross stitch national lottery oeis latex final fantasy news gerry anderson interpolation countdown braiding pythagoras inline code game of life video games light london sound trigonometry captain scarlet hats dates world cup programming binary harriss spiral probability chalkdust magazine people maths christmas card geometry rhombicuboctahedron game show probability triangles menace draughts php puzzles hexapawn craft reuleaux polygons london underground dragon curves frobel games manchester science festival realhats reddit chess machine learning folding paper aperiodical big internet math-off plastic ratio golden spiral misleading statistics approximation nine men's morris football bodmas pac-man books folding tube maps matt parker european cup estimation dataset tennis statistics mathsjam wool bubble bobble platonic solids noughts and crosses curvature the aperiodical mathsteroids stickers speed arithmetic weather station golden ratio chebyshev## Braiding, pt. 1: The question

**2016-06-29**

Since Electromagnetic Field 2014, I have been slowly making
progress on a recreational math problem about braiding. In this blog post, I
will show you the type of braid I am interested in and present the problem.

### Making an (8,3) braid

To make what I will later refer to as an (8,3) braid, you will need:

- 7 lengths of coloured wool, approx 50cm each
- Cardboard
- Scissors
- A pencil

First, cut an octagon from the cardboard. The easiest way to do this is
to start with a rectangle, then cut its corners off.

Next, use the pencil to punch a hole in the middle of your octagon and
cut a small slit in each face of the octagon.

Now, tie the ends of your wool together, and put them through the hole.
pull each strand of wool into one of the slits.

Now you are ready to make a braid. Starting from the empty slit, count around
to the third strand of will. Pull this out of its slit then into the empty slit.
Then repeat this starting at the newly empty slit each time. After a short time,
a braid should form through the hole in the cardboard.

I call the braid you have just made the (8,3) braid, as there are 8 slits and
you move the 3rd strand each time. After I first made on of these braid, I began
to wonder what was special about 8 and 3 to make this braid work, and for what
other numbers \(a\) and \(b\) the (\(a\),\(b\)) would work.

In my next blog post, I will give two conditions on \(a\) and \(b\) that cause
the braid to fail. Before you read that, I recommend having a go at the problem
yourself. To help you on your way, I am compiling a list of braids that are known
to work or fail at mscroggs.co.uk/braiding. Good luck!

### Similar posts

Electromagnetic Field talk | Braiding, pt. 2 | Christmas cross stitch | Logical contradictions |

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