mscroggs.co.uk
mscroggs.co.uk
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

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 "decagon" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Dec 2019

Christmas card 2019

Nov 2019

Christmas (2019) is coming!

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

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2019