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!
                        
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
@no: yes, although rectangles work surprisingly well
Matthew
                 Reply
Would square cardboard work better than a rectangle
no
                 Reply
 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> <logo>
To prove you are not a spam bot, please type "ratio" in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

polynomials cambridge puzzles databet matrix multiplication asteroids sound estimation geometry signorini conditions light turtles edinburgh frobel dinosaurs quadrilaterals go christmas card oeis football numbers cross stitch fractals folding paper pascal's triangle preconditioning live stream ternary flexagons martin gardner menace craft royal baby reuleaux polygons braiding numerical analysis triangles trigonometry inverse matrices exponential growth statistics speed folding tube maps map projections advent calendar the aperiodical realhats raspberry pi chebyshev game show probability arithmetic big internet math-off determinants tennis phd weak imposition correlation games logs manchester science festival mathsjam pythagoras computational complexity zines fonts reddit people maths machine learning finite group hannah fry simultaneous equations video games logic tmip chess talking maths in public squares guest posts crossnumber rugby bodmas london underground pi approximation day sport datasaurus dozen stirling numbers weather station matrices probability newcastle chalkdust magazine london draughts interpolation data pi radio 4 programming golden spiral pac-man plastic ratio hyperbolic surfaces noughts and crosses errors gaussian elimination coins christmas a gamut of games dataset sobolev spaces graph theory curvature boundary element methods anscombe's quartet python hats wave scattering misleading statistics news platonic solids data visualisation geogebra electromagnetic field final fantasy world cup runge's phenomenon mean national lottery books logo rhombicuboctahedron dragon curves 24 hour maths approximation matrix of minors countdown wool captain scarlet finite element method recursion accuracy gerry anderson harriss spiral error bars standard deviation nine men's morris hexapawn matt parker graphs pizza cutting php mathslogicbot royal institution bempp fence posts game of life latex manchester convergence mathsteroids propositional calculus youtube golden ratio inline code dates stickers bubble bobble sorting gather town european cup ucl javascript binary palindromes crochet matrix of cofactors

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024