Geometry in Origami

In the paper A Note on Intrinsic Geometry of Origami, Koryo Miura, Professor and Director of the Research Division of Space Transportation, says: 

“The mathematical expression of an origami process is a transformation of a flat piece of paper into a polyhedral surface which expresses something.”

The word origami means “fold” and “paper” in Japanese, and can range from basic shapes to extremely intricate folded designs and formations. While Koryo Miura’s paper focuses on the mathematical aspects of origami, this sentence jumped out at me immediately as a creative practitioner, and I can relate it to my own creative processes and results.

I have always imagined origami to be a personal venture and it is often referred to as an art rather than simply a hobby. This could be because it provides both mental and physical challenge and problem-solving, introduces you to geometry, symmetry and spatial thinking, and deals with shapes and clean lines. It instills the ability to follow instructions and listen carefully, but it can also bring a deep sense of satisfaction and catharsis if followed through, and it helps cultivate creative thinking. The element of trial-and-error teaches patience and persistence (if folded wrong, a piece can become difficult or even impossible to continue). It is a timeless practise, accessible to anyone with access to a sheet of paper, and holds appeal to both children and adults alike.

In the article Analysis of Design Application on Structural Model of Origami, by Hsun-Yi Tseng, it is believed that: 

“Origami started out as a traditional art form found in religious rituals and folk customs before evolving into a creative art for leisure and recreation.”

jentriangularbox

My own attempt at origami. I went for something fairly simple: a trinket box design I found a few years ago. It has been a while since I’ve folded this box and it took a degree of fiddling, studying the tutorial, and testing my own dexterity before I could finish it. While there are areas that need improvement (corners not quite closing), I am overall happy with the result and it was worth the time invested. This type of origami also has its practical uses – the box will hold paper clips, pins and other small pieces of stationary on my desk.

Returning to my earlier statement that I can relate expression through origami to my own creative processes, I found that folding this box focused my attention immediately. This is something that happens frequently when I begin a new design, whether its a practical or digital piece, particularly if there are intricate elements to it. Many designs rely of different parts coming together to create meaning and resolution.

The box was not without some frustration, with some of the flaps awkward to slot together, but once the triangular shape started to come through these frustrations lessened. Perhaps this is because I could see the box taking shape. 

In the book The Use of the Creative Therapies with Sexual Abuse Survivors, editor Stephanie L. Brooke writes:

“Another important therapeutic aspect of Origami is physical and psychological effect of the act of folding paper, which allows us to use the left and right spheres of our brains at the same time (Shumakor, 2000).”

Much like zen drawing and art therapy, origami can become a form of catharsis with its repetitive motion and tendency to focus attention. I frequently engage in ASMR (Autonomous Sensory Meridian Response) exercises as it relaxes my mind and body, and one of my main triggers is the folding, cutting, touching and manipulation of paper and card. Paired with the joy of solving a puzzle, creating a complex or beautiful design, and focusing attention, I can see why origami is used in art therapy and mindfulness practises to enhance a sense of wellbeing or help process a traumatic experience.

One of my favourite origamists is Ekaterina Lukasheva, whose manages to merge incredibly complex and precise modular designs with a great sense of movement and an organic feel:

ekatrina

I can’t help but think that she was inspired by naturally occurring geometry in the world around her, a topic I will blog about in a separate post.

Tomoko Fuse’s modular origami boxes are also worth noting, combining basic geometric design with gentle motion and peacefulness. The structure of the box itself creates the pattern, with no need for additional decoration or intricacies:

tomokofuse

The Sonobe Cube Lamp is another lovely and practical piece of origami, based on the Sonobe module (believed to have originated from Mitsunobu Sonobe and Toshie Takahama), and illuminated by Judith at Origami Tutorials:

sonobe-lamp

Also the beautiful Hydrangea Tessellation, originally created by Shuzo Fujimoto:

hydrangeatessellation

References

Brooke, Stephanie L. (2006): The Use of the Creative Therapies with Sexual Abuse SurvivorsCharles C. Thomas Publisher; 1st edition.

Miura, Koryo (1989): A Note on Intrinsic Geometry of Origami. First presented at the First International Meeting of Origami Science and Technology, Ferrara, Italy.

Tseng, Hsun-Yi (2017): Analysis of Design Application on Structural Model of Origami. Published in 2017 International Conference on Applied System Innovation (ICASI).

Learn how to fold the origami triangular box hereSee more of Ekaterina Lukasheva’s origami hereTomoko Fuse Modular Box hereOrigami Tutorials.

Discover ASMR. There are some incredible ASMR artists out there and they are easy to find on YouTube, but the ones I am always drawn back to are Charlotte Angel and Rhianna at ASMR Magic.

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