mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

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:
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 "c" then "o" then "s" then "i" then "n" then "e" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Sep 2019

A non-converging LaTeX document
TMiP 2019 treasure punt

Jul 2019

Big Internet Math-Off stickers 2019

Jun 2019

Proving a conjecture

Apr 2019

Harriss and other spirals

Mar 2019

realhats

Jan 2019

Christmas (2018) is over
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2019