Week 9 Activity + Connections

 

I watched two of the videos (one by accident but couldn't take my eyes away... then accidentally clicked on the second link and couldn't stop watching that). 

Watching De Vries's (2016) Quilting Mathematics video, I collected a few vocabulary words: 

Tessellation or Tiling of the plane: a collection of two-dimensional shapes (tiles) that fill the plane with no overlaps and no gaps. 

Monohedral: tessellations use 1 tile of same shape and size, example: squares (grid), equilateral triangle, hexagon

Dihedral: tessellations use 2 different tiles

Trihedral: tessellations use 3 different tiles

There are 15 known monohedral tilings of convex pentagons.

Periodic tessellation: a tessellation contains translational symmetry.

Aperiodic tessellation: a tessellation that lacks translational symmetry.

Sir Roger Penrose discovered an aperiodic dihedral tiling:

This section of creating symmetry by De Vries connects very well with Belcastro & Schaffer's (2011) dancing mathematics article. 

Cell: smallest element in the pattern that is repeated using the symmetrical operators (T,R,Mirror,G).

Unit: smallest element in the pattern that is repeated by translation. The cell and unit could be the same depending on the translation type.

There are 17 different symmetry groups. 

This example below shows the difference between how a quilter builds the quilt (left) and how a mathematician might analyze the quilt (centre). Their "units" would be different! The symmetry group is on the right.

To conclude her talk, De Vries states "Using mathematical concepts and algorithms in the design of quilts can lead to endless variety. Recognizing mathematical concepts in quilts can surprise, inspire and delight." After she introduced her special set of tapered triangles and the mathematical patterning required to develop her themed quilts, I can see how each variation was constructed with math in mind.

De Vries mentions that she creates and self-imposes rules on her projects to generate something non-random. I wonder if this is what she deems is a mathematical behaviour. Is mathematics the imposition of rules, categorization and structure? Perhaps that should be a piece of the criteria of the Math/Art Manifesto?

I agree with De Vries in that seeing a pattern with some inherent rule is more aesthetically pleasing than seeing something randomly strewn together. Even when observing colours on a virulent tulip there is structure on a cellular level. 

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I tried the Miura-Ori fold that is used by Uyen Nguyen's (2021) fashion design. I really wanted to create myself an origami garment, but unfortunately I ran out of time. I might update this in the future with some sort of attempt. These three shapes answered various questions I had:

Top: Does the paper need to be 'origami paper' (square in shape)? NO

Left: Can I use an entire piece of paper without modifying its dimensions? YES

Right: Can I use the bookmark strip of paper left from cutting a square to do this fold? YES

I asked my students in Earth Science 11 to fold this special fold as a "fun" activity connected to our Astronomy unit. My students did not find this entertaining or fun at all. They struggled hard trying to invert the mountain and valley folds. Following this video by MATU (2020):

This is what remains of their participation for the day. A battlefield of creased papers. Some took the time to complete the shaping and turned out really well. It was much harder than it looked, and I hope it helped them develop more of an appreciation of this skill and its application in Astronomy. 

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Screenshot from Burkard Polster's (2020) Mathologer video What is the best way to lace your shoes? Dream Proof.

I absolutely loved this video. Very entertaining and well explained. I have explored playing with shoe lacings before, but I found that unless they are the criss-cross, they take a substantial amount of time to tighten/loosen to put on/off. The mathematical analysis behind shoe lacings is very interesting. I definitely have more of an appreciation for tight lacings now.

Links to viewing & activities from the week:

Viewing:

1) Carolyn Yackel: How orbifolds inform shibori dyeing (Gathering for Gardner, Oct. 2020, 28 min)

2) Gerda de Vries (University of Alberta) Quilts as mathematical objects (PIMS, UBC 2016, 1 hr)

3) Uyen Nguyen, Origami Fashion Part 1 and Part 2 (20 min total. Uyen recently had a solo show at the Museum of Mathematics – MoMATH – in New York City!) [Optionally, you might also be interested in taking a look at Uyen’s related Bridges paper Uyen Nguyen (Bridges 2020) Folding fabric: Fashion from origami]


Activity:

Choose one of the following to try on your own, or with your students, family or friends this week!

(1) Four Burnaby secondary math teachers (Goeson, Nicolidakis, Gamble and Houghland) developed this curricular work with Coast Salish weaving and mathematics. If you haven't worked with this before (at Indigenous Math Day at UBC, for example), here's a chance to give a try to weaving mathematics.

(2) Try out Miura Ora Origami (the technique Uyen Nguyen uses in her fashion design). Here are two instructional videos (A and B) -- and feel free to find other instructions if that suits you.


(3) Or for something completely different, try a variety of mathematically-interesting (and efficient) ways of lacing your shoes, as described in this Mathologer video!

References:

Belcastro, S. M., & Schaffer, K., (2011) Dancing Mathematics and the Mathematics of Dance. Math Horizons. 18(3). pp. 16-20. DOI: 10.4169/194762111X12954578042939

De Vries, G. (2016, August 18). Making mathematics with needle and thread: Quilts as mathematical objects [Video]. mathtube.org. https://www.mathtube.org/lecture/video/making-mathematics-needle-and-thread-quilts-mathematical-objects

MATU. (2020, November 9). Miura Ori - Traditionelle Miura-Faltung [Video]. YouTube. https://www.youtube.com/watch?v=EEGmnKKKhrk

Nguyen, U. (2021, January 7). Origami Fashion with Uyen Nguyen Part 1 [Video]. YouTube. https://www.youtube.com/watch?v=i4AoN1DtH6I

Nguyen, U. (2021, January 7). Origami Fashion with Uyen Nguyen Part 2 [Video]. YouTube. https://www.youtube.com/watch?v=bD7vUhdyO34

Polster, B. (2020, June 20). What is the best way to lace your shoes? Dream proof [Video]. YouTube. https://www.youtube.com/watch?v=CSw3Wqoim5M