1d to 3d part 2

 

1. Original purpose for jig: irregular hex structure makes converging pairs.

2. Hijacked for a different purpose: diverging pairs.

3. And a third possibility: radial pairs.

4. The 3 parts from the 19 degree angle jig highlighting mismatch.

5. Parts from the 20 degree jig - The converging pair model still has sticks converging at a point, and the other 2 models are now compatible.

6. Maths showing how the 20 degree configuration works. For compatibility B = C, see also pic 13 for diagrams of shapes.

7. Last night's inspiration: Vertex connected tetrahedron, sides have a regular hexagon as the structure at the centre.

8. Tetrahedron from 7, and a vertex connected tetrahedron with mixed sides, 2 as per 2 and 2 as per 3. 

9. Side connected tetrahedron, diverging sides

10. Side connected tetrahedron, radial sides.

11. Side connected tetrahedron, sides are a mix of pics 2 and 3.

12. Alternate view of 9.

13. Centreline sketches of items 1, 2 and 3, and compiled view used to work out geometry. Sizes from central sketch were used to design the jig MKII.

Hi

Since my last post, I have been progressing quite well, making mostly abstract structures from  coffee stirrers and segments of drinking straws. I've posted on my instagram more often than blogging, so if you want to catch up a bit then head on over there.

But some new developments seemed quite interesting, and I wanted to write in a longer form than insta allows.  I had 3d printed and used a few different jigs to make sides for polyhedra, but had generally only made one type of shape per jig. Then a few nights ago I started exploring, making radially symmetric parts for example. 

Soon after developing a range of parts (pics 1, 2, 3) that could come from an irregular hexagon jig, I realised that with a bit of tweaking, 2 of the parts could be compatible in structures. Not only that, they could be put together in 2 ways (edge connected and vertex connected) in all the platonic solids that have triangles as faces, that is tetrahedrons, octahedrons and icosahedrons.

Sofar I have just made tetrahedrons in this specific way, and a few samples are shown above.

The tweakage to get the type 2 and 3 sides to be compatible was changing the angle between coinciding sticks (type 1) to 20 degrees form 19. 20 degrees is exactly right and I stumbled on this angle by guesswork but later proved it to be correct with a surprisingly simple method I am very proud of (pics 6 and 13).

Not sure what I'll build next and I hope you enjoyed this slightly longer form of description.

Regards

 

Steve Nurse 

1d to 3d

Display at Bridges Eindhoven...

 

included this 1d to 3d dodecahedron

My setup on the opposite side of the hall.

Some art inspiration from England......

and from home. I took this photo to finish an article I have written.

Septagonal face in 3d printed jig.

Hexagonal and Pentagonal faces

Everything including a pentagonal face construction from spokes.

The flower shaped jig was a first off attempt, Bit of a problem there, the floback clip would need to be removed through the wooden assembly.

New materials

Soaking sticks for the 7 sided figure. Soaking makes them more pliable and so they can bend more without snapping.

Hi

Recently I attended the Bridges Maths and Arts conference in Eindhoven in the Netherlands. It was great and I will report further in other posts. But for now I'm reporting on some Bridges inspired stuff.

Next to the main Bridges conference hall was an informal poster area where I set up camp at a table to show and discuss some of my 3d printed things.  I was intrigued by some of the displays including one of (basically) one dimensional wooden blocks transformed into a dodecahedron. Unfortunately I didn't get the contact details of the gentleman who had made them. The work was made simpler by connecting the pentagonal faces at the midpoint of sides instead of at the dodecahedron vertices. Also a young relative in England made some intriguing related artwork!

On getting home to Melbourne, I started working on similar 1d to 3d constructions and plan to ferret around in the maths of the things soon. To make the 7 pointed star shown above, I needed to cut the craft sticks I had in 2 parts lengthways, soak the sticks, and also assemble them on a 3d printed jig.

Since then I have sourced some better craft sticks. On a trip to Northcote Plaza for a haircut, shopping, lunch and banking I also bought (hooray) some coffee stirrers which to me are just longer skinnier craft sticks. Their full name is "Premium Quality Eco Wooden Catering Coffee Stirrers" (!) Anyway with these it should be simple to make more models and more elaborate models. Hopefully by next week I can report on some 3d constructions,

Regards Steve Nurse  

 After a bit more work (ok its not work, just mucking around with the craft sticks) I have managed to make 2 of the platonic solids, the tetrahedron and the octahedron using 6 craft sticks per side. The inner circle of 6 stick crossings is glued to hold the shape together while the outer circle of crossings is left unglued: these crossings clamp onto cardboard which forms edges.

I've made a spreadsheet which works out the geometry of the faces based on the length of the  craft stick, the number of sides in the central polygon, and which stick ends coincides. From that spreadsheet its reasonably easy to draw and guess the feasability of various designs.  I'm not sure what I'll make next.

Update September 29

After giving one of my current lampshades to a friend I had a lampshade vacancy, so decided to make one from my current techniques with (mainly) craft sticks. Mk1 was a cube and I later expanded on it to make a 2 cube version. On mkII the translucent screen is baking paper. There are 10 sides in all on mkII, and I have left 6 of them open. The lamp is always against the wall, and the shadows of the craft sticks on the wall are a feature of the shade.  Craft sticks, baking paper, staples, glue, cut up manila folders.

 

Review: Fear of Mathematics

1. Maths is not arithmetic however fluency with arithmetic can help maths. Maths learning starts when maths related concepts are observed and discussed in everyday life.

 

 

2. Maths is a processing art in the same way that cooking is. Skill and knowledge are needed to distill ingredients into delicious meals and there is a parallel in processing situations using mathematical understanding.

3. Some art forms cut to the chase and are the condensed version of others. This is true of prose and poetry, of descriptions and mathematical descriptions, and why I have attempted to use diagrams to explain Auerbach's work

This is an illustrated review of “The fear of mathematics and how to overcome it” by Felix Auerbach. Although the book was written in 1924, it was only translated into English a century later, in 2024. Its original German title is Die Furcht vor der Mathematik und ihre Uberwundung. At 104 pages it is fairly short, and few of the pages are taken up with translator’s notes and a short biography of Auerbach.

Nevertheless, the book resonated with me as a part-time educator, engineer and amateur mathematician. It could equally well have been titled “What mathematics is – and what it is not”. To get the message, the book needs to be read carefully, and although this book asserts that mathematics is poetical, taken as a whole it is hard to digest. For example, these sentences are related to the differences between arithmetic and mathematics:

“But when one then says, as happens repeatedly, that the pursuit of mathematics mechanizes one's spirit takes away one's freedom and forces us into pre-determined schemata, that is another egregious misunderstanding. It's the result of another piece of legerdemain.” and are wordy and not very poetical!

 Because I was keen to understand, and sympathetic to the arguments, I found myself visualising the words as diagrams and pictures. Some of these I jotted down on paper, they may help with an understanding or discussion of the book. Overall I thought the book worthwhile and full of concepts every maths educator, engineer, scientist and designer should be familiar with.

Ordering is through the website for the book, https://www.thefearofmathematics.com/

4. At the heart of every subject is a mathematical core or skeleton. An understanding the maths of a subject is vital and such a part of our world that everyone should be capable of it.

5. This can be expressed in another way: the blue figure has overcome fear of mathematics and is better able to see the true nature of arts and sciences. This is expressed more poetically by Auerbach, "Whoever knows how to read the language of mathematics is like the legendary Young Siegfried; they can commune with all the birds of the forest and the fields, and discover the secrets of nature, which remain forever unrevealed to people who are under the spell of lexical language."

A work involving artistic technique and maths can involve two methods, the artist can consult with a mathematician or the artist can acquire the mathematical knowledge. Auerbach prefers the second of these methods which leads to and expansion of the artists practice through knowledge.