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Math and Intuition in Origami Design

In an interview with Mark Kirshenbaum for Origamigos (see video and transcript below), he expressed his thoughts and experience about the relationship between math and origami design.

I’d like to share an excerpt of our conversation as an example of the content being offered in ORIGAMIGOS, the Origami Spirit membership.

You may be surprised by Marc’s response to my question regarding the use of math for paper folding as he designs his models!

Marc Kirschenbaum is a leading American origami artist. He has covered a wide range of subject matter and has utilized a variety of folding mediums.

His origami work has been shown in many museums and shows around the world, including the American Museum of Natural History, The Smithsonian, Mingei International Museum, and Hangar-7.

Marc’s published origami books include:

In addition to talking about origami and math, in our hour-long discussion we touched on different topics:

  • Origami commercial work
  • Connections between music and origami
  • Influences and connections: Spanish sculptor, Miguel Ortiz Berrocal
  • Influences and connections: USA Artist, Jeff Koons
  • How to handle people’s comments about the practice of origami
  • Pure and simple origami
  • “Pureland” definition and history
  • Models of Marc’s design that are particularly significant and why
  • How to encourage people to start creating their own origami figures
  • How to help people who become discouraged by the difficulty of folding a particular model

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Math and Intuition in Origami Design

An excerpt from my interview with Marc Kirschenbaum

LT: Interview excerpt with Marc Kirshenbaum, Math and Intuition In Paperfolding and Design. This is Leyla Torres of origamispirit.com. To watch the full interview with Marc Kirshenbaum, see other exclusive interviews and video tutorials, sign up for Origamigos, the Origami Spirit membership.

So, to do a little introduction, Marc Kirshenbaum I’ve known for a long time through origami USA. We both belong to the same organization and I have been following his origami career for a long time. He has a lovely website which is called… 

MK: Sakura Origami 

LT: SakuraOrigami.com. You can check all his publications there. You said that that you like to approach the designs of your models as a math problem. How much math do you use? Do you use any in the designing of your models?

MK: Well, as little as possible. I really… I mean it’s funny, I remember…this is years ago… I don’t know if anyone is familiar with Erik Demaine––he won the genius award––and he was fascinated with this chessboard I came up with and he wanted to just pick my brain. At the same time, I was very excited to learn that what he was doing. And he told me that I have a very mathematical mind, which I found sort of interesting because I was never great with the mechanics of math.

But you know in terms of computational things is and all that, but in terms of, I guess higher level things and be able to attack a problem that I was pretty good at. And there is an element of that when I’m designing things but… I mean, I feel fortunate that I started origami at a young age and it’s… a lot of it’s intuitive at this point. There is, you could say, an approach I take when I when I design things, and I have an expectation of what’s going to work and what doesn’t. But I try to avoid hardcore mathematics if I can. But it does come up. Probably most recently… my wife and I were joking about that for a while in my Pureland book, which is supposed to be simple models, for sure, I was using a ton of mathematics, just to figure out how to get everything to align nicely. Not perfectly satisfactory, but… I would just… constantly solving problems.

LT: That’s great and it’s interesting and it’s something that I would like we all to think about, about the mathematics. I have a sister who’s a mathematician and she loves numbers, and she did Computer Science and Mathematics as a degree. And I always thought that my… you know, mathematics always gave me this sense of stress, you know, like I have to perform, I have to take an exam I have to come up with these answers… but, at the bottom of it I didn’t think that I was too bad for math… you know, I could deal with it, but once I became more interested in origami I realized that I do have that mathematic mind in a very––as you say––in a very intuitive way. So that’s something that I’d like to highlight from what you just said, not that it is not only the mathematical mind that needs to do the numbers but the mathematical mind that can feel and follow and solve some problems.

MK: Yeah, and in origami, there’s there’s no necessarily right answer. There are just different answers.

LT:  Right. Right Exactly.

MK: So, it’s a great way of exploring, you know, I guess… concepts and seeing relationships of shapes. It’s fascinating stuff and if you’re good at math and you could actually apply to it, you could see a lot of things in a clear way. The problem with mathematics as it’s taught in schools is that if you just see a lot of numbers and some symbols but when you actually apply it, which is what’s often happening in origami, it starts to come to life and you see it and it makes it easier.

LT: Yeah, so you mentioned your book, Pure and Simple Origami. Do you have a copy there with you by any chance? That you can show us the cover?

MK: Yes.! Hopefully this can be seen. This literally came in the mail today. I finally got my hardcover version. Very excited about this one. 

LT: Yeah, I haven’t gotten my copy yet but… one of the reasons I would buy that book alone is because of this little car.

MK: Oh, yes!

LT: Mark happened to teach it in the Foldspace convention. We both were teachers there and I just adored the car. 

MK: Thank you.

To watch the full interview with Marc Kirshenbaum, see other exclusive interviews and video tutorials, sign-up for ORIGAMIGOS, the OrigamiSpirit membership.

Marc Kirschenbaum’s Origami Car


This interview excerpt is an example of the content being offered within the ORIGAMIGOS membership. Also included within the membership are exclusive tutorials, printables, and an engaged and supportive community.

ORIGAMIGOS welcomes paper-folders at any skill level from NOVICE to EXPERT to explore aspects of origami as a mindful, educational, artistic, entertaining, and intellectual practice.

Click here to see all the benefits you will enjoy as an ORIGAMIGOS member.

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