3D Math as Art – Paper Tori by Kris Koch
As those of us in the northern hemisphere hurtle toward Winter Solstice and many other celebrations that take
place at this near-magical time of year, I have to say the topic for
today's post, along with its ethereal images, could not have dropped into my inbox at a better time. Kris Koch, the
maker and photographer of paper sculptures that prompted thoughts about the joys of increased light and longer days, was a recent Paper Connection itajime giveaway winner. When Kris replied to my message telling her she had won, she was thrilled, of course, and casually mentioned her new-to-me type of paper art. We struck up a conversation and this post is a result of my education, a la Kris, about paper tori.
In a nutshell, this is what Kris told me: I’d love to talk to you about my paper sculptures. I design and create tori and other geometrical shapes. I’m also a photographer and have been doing some movement studies. I’ve been inspired by origamic architecture, especially the work of Yoshinobu Miyamoto. When I get intensely interested in something, I go all out with research.
What follows is an interview that explains her intriguing work and process... enjoy!
What is a torus?
A torus (plural, tori) is a 3D geometric shape that closely resembles a doughnut or bagel, complete with center hole. What I love about tori is their unusual symmetry. I also find that looking at them is quite meditative.
How did you become interested in the art and craft of paper?
My lifelong passion for paper began with origami and simple paper-cutting projects, such as snowflakes and Swedish woven hearts. I have amassed an extensive paper collection and in my desire to use it creatively, about five years ago began to research more complex paper art. Throughout this process, I’ve been incredibly inspired by the work of several amazing artists, including Anna and Lene Schepper (Paper Matrix), Carol Parsinnen (Extreme Cards and Papercrafting) and especially Professor Yoshinobu Miyamoto, a Japanese design engineer.
Why paper?
I love the transformative and dynamic potential of paper. Creating 3D geometry requires a medium that is both flexible and strong. Paper fulfills this requirement and more. It’s also lightweight, inexpensive and readily available. As someone who learns by doing (and making LOTS of mistakes), paper has been the perfect medium on which to practice this craft.
What do you mean by a 6, 8 or 12-ray torus?
The template I use to create my tori is basically a slotted puzzle. Half of the pieces have slots on the top and half of them are on the bottom. The rays refer to the number of pieces. It’s possible that there is an official math/engineering term for this, but if so, I haven’t yet found it. A 6-ray torus will have 6 top pieces and 6 bottom pieces, an 8-ray torus will have 8 top and 8 bottom, etc. More pieces generally equates to more sturdiness and more complex geometric symmetry.
How do you create your work?
Right now, I use a Silhouette desktop plotter/cutter and design my templates on the tool’s native software. However, very soon I’ll have outgrown its production capability in both output and the range of materials it can handle, so I’m researching professional-grade cutting machines.
What is your background?
I have a Master’s Degree in Adult Education and have worked in non-profit environmental education and higher education for the past 16 years. However, I recently decided to make a career change and work to live, rather than live to work. Toward that end, I’ve been laying the groundwork to make a living in the creative arts (I’m also a photographer.) Along with my Etsy shop, I have Instagram accounts - @naturenougat and @kitakoch - that feature my fine art photography and photos of my paper creations.
Tell us more about these beautiful translucent photographs.
They are part of a photographic study of movement and symmetry on which I’ve been working. I hope to include them in a show in 2017 or 2018.
In a nutshell, this is what Kris told me: I’d love to talk to you about my paper sculptures. I design and create tori and other geometrical shapes. I’m also a photographer and have been doing some movement studies. I’ve been inspired by origamic architecture, especially the work of Yoshinobu Miyamoto. When I get intensely interested in something, I go all out with research.
What follows is an interview that explains her intriguing work and process... enjoy!
What is a torus?
8-Ray Torus
A torus (plural, tori) is a 3D geometric shape that closely resembles a doughnut or bagel, complete with center hole. What I love about tori is their unusual symmetry. I also find that looking at them is quite meditative.
How did you make your first torus?
I started from scratch. I printed out an online template, and armed with an old protractor, I measured everything by hand and spent a lot of time relearning basic geometry. Then came the challenge of transferring that knowledge into a design program to create my own templates that could be precision cut by computer. This was a fairly long process filled with trial and error, but I am a creative problem solver by nature and had a lot of fun figuring it out.
I started from scratch. I printed out an online template, and armed with an old protractor, I measured everything by hand and spent a lot of time relearning basic geometry. Then came the challenge of transferring that knowledge into a design program to create my own templates that could be precision cut by computer. This was a fairly long process filled with trial and error, but I am a creative problem solver by nature and had a lot of fun figuring it out.
Torus Angles
How did you become interested in the art and craft of paper?
My lifelong passion for paper began with origami and simple paper-cutting projects, such as snowflakes and Swedish woven hearts. I have amassed an extensive paper collection and in my desire to use it creatively, about five years ago began to research more complex paper art. Throughout this process, I’ve been incredibly inspired by the work of several amazing artists, including Anna and Lene Schepper (Paper Matrix), Carol Parsinnen (Extreme Cards and Papercrafting) and especially Professor Yoshinobu Miyamoto, a Japanese design engineer.
Puzzle Ball
Why paper?
I love the transformative and dynamic potential of paper. Creating 3D geometry requires a medium that is both flexible and strong. Paper fulfills this requirement and more. It’s also lightweight, inexpensive and readily available. As someone who learns by doing (and making LOTS of mistakes), paper has been the perfect medium on which to practice this craft.
Where do you find creative inspiration?
That’s easy: Nature! I’m endlessly inspired by natural design engineering. From petal arrangement on flowers to seed shape and dispersal methods, I am amazed at the structures and survival strategies found in natural organisms. While I’ve seen and/or created templates for 5, 8 and 12-ray tori, I just finished designing a 6-ray torus because snowflakes have 6-sided crystals and I wanted my creations to be scientifically accurate. Now that I have the basic template worked out, I’ll start on the snowflake designs.
That’s easy: Nature! I’m endlessly inspired by natural design engineering. From petal arrangement on flowers to seed shape and dispersal methods, I am amazed at the structures and survival strategies found in natural organisms. While I’ve seen and/or created templates for 5, 8 and 12-ray tori, I just finished designing a 6-ray torus because snowflakes have 6-sided crystals and I wanted my creations to be scientifically accurate. Now that I have the basic template worked out, I’ll start on the snowflake designs.
6-Ray Torus
What do you mean by a 6, 8 or 12-ray torus?
6-Ray Torus Template
The template I use to create my tori is basically a slotted puzzle. Half of the pieces have slots on the top and half of them are on the bottom. The rays refer to the number of pieces. It’s possible that there is an official math/engineering term for this, but if so, I haven’t yet found it. A 6-ray torus will have 6 top pieces and 6 bottom pieces, an 8-ray torus will have 8 top and 8 bottom, etc. More pieces generally equates to more sturdiness and more complex geometric symmetry.
Heart Wreath Torus
How do you create your work?
Right now, I use a Silhouette desktop plotter/cutter and design my templates on the tool’s native software. However, very soon I’ll have outgrown its production capability in both output and the range of materials it can handle, so I’m researching professional-grade cutting machines.
What do you do with your creations?
I sell my work at local art galleries, museum stores and consignment shops. I also just opened an Etsy shop, NatureNougat, that will feature nature-inspired torus ornaments, sculpture and more.
I sell my work at local art galleries, museum stores and consignment shops. I also just opened an Etsy shop, NatureNougat, that will feature nature-inspired torus ornaments, sculpture and more.
Gold Snowflake Torus
What is your background?
I have a Master’s Degree in Adult Education and have worked in non-profit environmental education and higher education for the past 16 years. However, I recently decided to make a career change and work to live, rather than live to work. Toward that end, I’ve been laying the groundwork to make a living in the creative arts (I’m also a photographer.) Along with my Etsy shop, I have Instagram accounts - @naturenougat and @kitakoch - that feature my fine art photography and photos of my paper creations.
Allium Torus
Tell us more about these beautiful translucent photographs.
They are part of a photographic study of movement and symmetry on which I’ve been working. I hope to include them in a show in 2017 or 2018.
Fascinating! Thanks for sharing Kris' work. It's amazing.
ReplyDeleteThese are so intriguing - and, of course, visually stunning.
ReplyDeleteThanks so much for sharing - the interview was very illuminating - no pun intended. LOL
I have always loved math and don't understand why anyone wouldn't. I wonder if it was related to art, whether there would be any converts?
ReplyDeleteI will keep an eye on Kris and her work. Maybe I can work it into conversation with some math haters.
Thanks for your comments, Cindy, Tristan and kitblu - I'm glad you enjoyed seeing Kris's tori. kitblu, I think you're onto something about art helping to take away math-fear... definitely worth a try!
ReplyDelete