An orderly tangle

A paper version, I haven't made this yet, just cut the pieces.

Hi

After a few weeks of trying, I have managed to make my first "orderly tangle" or "regular polylink" which is a type of link (lots of loops tangled up) made by rotating and interlinking regular polygon shaped loops on the face of a solid. These shapes are described in a book by Alan Holden called (unsurprisingly) Orderly Tangles.  I have written and submitted an article on twin edge polyhedral links and knots (see my last post ) , and during the review process, Holden's work was recommended to me. After resubmitting the article and also seeing online examples, I decided to have a go myself. There are articles by George Hart describing paper and other tangles here and here , but the one I made was based on Alan Holden's work. From here I might be able to work out the maths of the things and could go on to make them from other materials (beer cans being seem to me the most obvious).

Anyway my steps were - 

* Get a copy of Orderly Tangles, I needed to do this for my article anyway.

* Work out what I wanted to make. (This was an easy choice, I had made topologically similar cubes before)  

* Look up the dimensions needed and stick to the proportions - I used 1/4" = 10mm as a scale.

* Replicate the squares Holden used in a 2-part 3d print - 2 identical C shapes plug into each other.

* Attempt assembly without jig (really hard, I mucked around and made "other stuff" with the 12 pieces instead.

* Go back to the original photo and work out the proportions of a jig - it could be based on a 16mm square rod about 100mm long.

* Design and print a cross-shaped jig that could come apart from inside the polylink

*  Strap 2 squares to the jig with rubber bands, and keep putting more squares on as per the photo. To assemble the last square in I had to crop the pin on each side by about 5mm, the fit was too tight otherwise.

* Disassemble the jig et voila!

Regards Steve Nurse

For 3d print files see https://www.thingiverse.com/thing:7366096  

 

 

 

 

Topology Lecture at Monash

 

With Dan at lunch, I'm in blue

Took some unsuccessful steps to not get lost, I had this as a phone photo.

Huntingdale Station

The new routes explained

The blurb and 

several part-pages from the presentation,

Hi

 After more than a year of work and discussions with the publishers, I am hoping some of my maths work will be officially released soon. I haven't waited around though and when reviewers asked "has the work been used in education?", I had to say no, but then went on to ask my University maths contacts if I could present the work. After a few days, Daniel Mathews of Monash came through and invited me to speak to Monash postgrad topology students and researchers. I was most honoured, said yes, and got working on my presentation about a week before the due day.

It all came together quite well. By the night before the presentation, the work was finished and I'd rehearsed and even timed it. On the day itself, I headed off by bike, through some rain, but with a rain jacket on so no real stress. There were new (to me) arrangements for Dandenong line trains which I had to negotiate but that wasn't too hard either. Unfortunately I got off at the wrong station (Clayton not Huntingdale) and spent a bit of a confusing time getting a bit lost before finally reaching the maths building. I remembered it even after 10 or so years, had a rest, a bread roll and some water in the lobby, then went up to meet Dan.

The lecture went well. Having mild stress (rain, train changes, getting a bit lost) before the lecture didn't hurt and I got through it all quite well. The only questions were about "chamfering", which most of the students hadn't heard of. After the lecture I was shouted lunch by the maths department which went well, and then one of the students and I had a maths chat. After that it was back on the bike and home. This time I managed to get straight to Huntingdale and was whisked home pretty quickly and without suffering under deluges.

This link takes you to the Thingiverse page where last week's talk, a preprint of the full article and parts for constructions (as 3d printable stl files) are all available. I welcome any correspondence and questions!

 Regards Steve Nurse