Braiding, pt. 1: The question

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:
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.

The problem

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 Good luck!

Similar posts

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


Comments in green were written by me. Comments in blue were not written by me.
@no: yes, although rectangles work surprisingly well
Would square cardboard work better than a rectangle
 Add a Comment 

I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "decagon" in the box below (case sensitive):


Show me a random blog post

Jan 2021

Christmas (2020) is over
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼


platonic solids cross stitch tennis preconditioning pi php fractals binary computational complexity phd mathsteroids wave scattering approximation a gamut of games matrix of cofactors coins tmip palindromes the aperiodical talking maths in public puzzles radio 4 exponential growth inverse matrices flexagons matrix of minors python bubble bobble interpolation national lottery hexapawn pi approximation day plastic ratio numerical analysis propositional calculus golden ratio pythagoras chess latex big internet math-off pizza cutting manchester matt parker go countdown quadrilaterals javascript trigonometry twitter pac-man advent calendar logic bempp arithmetic estimation world cup game of life noughts and crosses asteroids dates finite element method light royal institution accuracy dragon curves wool curvature error bars books statistics programming squares weather station bodmas graph theory ucl misleading statistics matrices cambridge gaussian elimination final fantasy raspberry pi menace sobolev spaces rhombicuboctahedron sport logs chebyshev people maths harriss spiral london underground determinants football royal baby news stickers machine learning polynomials geogebra map projections boundary element methods realhats reddit electromagnetic field gerry anderson mathslogicbot braiding probability golden spiral rugby triangles data visualisation graphs craft nine men's morris speed simultaneous equations frobel oeis game show probability convergence signorini conditions inline code matrix multiplication manchester science festival christmas sorting ternary folding paper chalkdust magazine european cup data mathsjam reuleaux polygons london dataset weak imposition hats sound folding tube maps christmas card video games captain scarlet games martin gardner draughts geometry hannah fry


Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021