Math Art History: Miura Folding

Topic: Miura folding (Miura-ori)

Group members: Michelle and Yiwei

    In 105AD, Cai Lun invented and innovated paper that is affordable and foldable. Since then, paper folding became a folk art in China. Then, in the 6th century, the paper was carried to Japan by Buddhist monks and Origami art was popularized by the Japanese a thousand years later. In 1797, a Buddhist abbot 義道一円 published the first Origami book Senbazuru Orikata (i.e. Secret to Folding One-thousand Crane). The modern art of Origami was promoted by Akira Yoshizawa, known as the master of Origami. He has published 18 books and created over 50,000 Origami models. In addition, the book Sadako and the Thousand Paper Cranes by Canadian-American author Eleanor Coale, based on a true story, made Origami more accessible to a wider audience. Today, origami is widely used in fashion design and science. The most important of these is the application of Miura folding to the large solar panels of space satellites. Yiwei and I have created artwork with Miura Origami and we hope that our students will also be able to participate in this artwork (there will be a surprise on our presentation day).

References:

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Bain, I. (1981). The Miura-Ori Map. British Origami Society. Retrieved from

https://britishorigami.info/academic/mathematics/the-miura-ori-map/. 

Georgia Institute of Technology. (n.d.). History of origami. Paperdev Gatech Edu. Retrieved from https://paperdev.gatech.edu/kinetic-joy/history-origami. 

Li, Y., Liu, W., Deng, Y., Hong, W., & Yu, H. (2021). Miura-ori enabled stretchable circuit boards. Npj Flexible Electronics, 5(1), 1–9. https://doi.org/10.1038/s41528-021-00099-8 

Mitchell, D. (n.d.). A brief outline of origami design history. David Mitchell's origami heaven. Retrieved from http://www.origamiheaven.com/origamidesignhistory.htm.

Nishiyama, Y. (2012). Miura folding: Applying origami to space exploration. International Journal of Pure and Applied Mathematics, 79(2), 269-280. 

Schenk, M. & Guest, S. D. (2013). Geometry of Miura-folded metamaterials. Proceedings of the National Academy of Sciences - PNAS, 110(9), 3276–3281. https://doi.org/10.1073/pnas.1217998110 

Suto, Adachi, A., Tachi, T., & Yamaguchi, Y. (2018). An Edge Extrusion-Approach to Generate Extruded Miura-Ori and Its Double Tiling Origami Patterns.

Burger, A. P. (2019). Combining Two Pictures on a Miura Fold. Bridges 2019 Conference Proceedings, 419-422.

Artistic format:

Although we mentioned Origami several times in both EDCP342 and EDCP442 classes, we did not have a close look at its history. We decided to explore more on it and we would like to create an Origami art that involves Miura folding. During our presentation, we plan to include an activity to teach our classmates how to make a Miura folding art, so they can introduce this amazing idea to their students in the future. 

Class Presentations Nov. 10 + 15 - Math History

Nov. 10, 2021

    Nadine talked about how the speeds of church bells could be changed by studying its permutations.  Using factorials, the number of permutations of bells in "change ringing" could be examined.

    Alan researched about measurement and talked about how the human body was used to measure things that are used by human bodies.  We still use our bodies to measures things since it is portable wherever we go.

    I found the roots of probability interesting.  Jenny presented how it originated from games with dices to predict the future while fortune-telling was popular.

    Jordan differentiated between traditional logic and algebraic logic.  I found this interesting because I never explicitly though about how logic can be categorized into types.

Nov. 15, 2021

    In my presentation, I found that pascal's triangle appears in many countries in different forms and are known by different names.  I was reminded about this in Austin's presentation where a single combinatorics question was shown presented in different cultures with slightly different wording.

Ivan talked about how the term "league" was used by the Ojibwa people to represent the measurement of everything.  This is interesting because it caused a lot of confusion, but it continued to be used.

Yiru researched about Cavalieri's Principle, stating that if two or more figures have the same cross sectional area at every level and the same height, then the figures have the same volume.  I think this would be a great exploration activity for students. 

Trivium & Quadrivium

    In the article, St. Augustine "defends...the principles of logic as the inviolable foundations of knowledge" and using logic, we "find the truths of mathematics", that are "necessarily and unconditionally true; they cannot be contested".  Even now, there are truths in the world and in math that cannot not be proved fully.  There will always be something that we see is true, but cannot directly prove.  I find what St. Augustine said interesting because this idea has held through centuries.  Perhaps it is because it is an example of an absolute truth and it has proved itself to be so through the test of time.

    I found it interesting how they grouped subjects like music, arithmetic, and astrology together in quadrivium and grammar, logic, and rhetoric made the trivium.  I wonder how this trivium-quadrivium division was made and by whom.

Dancing Euclidian Proofs

    I was surprised that the idea of incorporating Euclidean proofs into dance was done so effectively.  I think it worked and it showed how these ideas can be presented by our bodies and nature.  I also found it surprising that the article mentioned how math can be seen in the two dimensions of time and space.  Dance and math catches the attention of the viewer in a presentation that is temporary and easily missed if you aren't paying attention.

    If the activity, "dancing Euclidean proofs", was used in a high school classroom, I think it would be surprising for many students.  I think it is very different from what most math classrooms are doing and that could attract the attention of students.  Through teaching, I found that doing out of the ordinary activities make things stick better.  

    I believe it would work best in small groups in a class where students are comfortable with each other.  In classes that have more students who do not know each other well could see lower participation and engagement in the activity.