mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Archive

Show me a random blog post
 2019 
 2018 
 2017 
 2016 
 2015 
 2014 
 2013 
 2012 

Tags

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

Archive

Show me a random blog post
▼ show ▼
 2016-06-29 

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 mscroggs.co.uk/braiding. Good luck!

Similar posts

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

Comments

Comments in green were written by me. Comments in blue were not written by me.
 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 "hexagon" in the box below (case sensitive):
© Matthew Scroggs 2019