Robert Lang

Eric Demaine is one of the better intersections of origami and mathematics, you should also read up on Dr Robert Lang, the OG and perhaps the most famous American JPL-physicist-turned-origamist: https://langorigami.com/ On the flip side the late Eric Joisel created perhaps the most amazing curved-crease and natural folding that we’ll ever see, his works were truly amazing art: https://ericjoisel.fr/en/home/

I'm an aspiring inventor of board games, so that takes all my free time. In the past, I used to practice technical origami: The ancient art of paper folding meets mathematics. It's the best of both worlds: a very practical, yet mind-bending activity. If you're interested, start by reading Robert J. Lang http://www.langorigami.com/ and Erik Demaine http://erikdemaine.org/. Origami Design Secret is the best introduction on modern techniques: http://www.amazon.com/Origami-Design-Secrets-Mathematical-Methods/dp/1… I also read a lot. It's not cool yet, but it will be if I get to read 100+ non-fiction books in one year. That's my goal for 2015.

Great article, thanks for sharing! Lang is a gem, and definitely my fave celebrity Origami artist (what a world). He has a website with both his art and scientific work, for anyone who's curious for more: https://langorigami.com/math-science-posts/

Here's another great video with Robert Lang discussing 11 levels of complexity of Origami. https://www.youtube.com/watch?v=MDwPXRy9IFc Ok, spoke too soon. Robert Lang does have lots of books on Origami https://langorigami.com/publications/my-books/

Good to see origami on the front page. For those who are interested in the field - whether as art, for the fun of folding or the various potential practical applications - the best book on the subject by far is Robert Lang’s Origami Design Secrets[1], which is a fantastic read and covers all of these and more. Lang is a mathematician at heart but also a consummate artist. I certainly can’t recommend origami enough as a hobby. [1] https://www.langorigami.com/publication/origami-design-secrets-2nd-edi…

Most anyone can "do" origami given instructions. But no one came up with a single fold design until David Mitchell did -- minimalist designs are only easy in hindsight. At the other extreme we have Robert Lang's amazing creations (which may require many more than four complex parameters!). http://www.langorigami.com/artworks/mammals

It's worth checking out Treemaker by Robert Lang. He is an origami master and his is the first of such programs. It's great to see paper-folding algos reach Blender 2.79, but I have immense respect for pioneers in the field. http://www.langorigami.com/article/treemaker

Is there? I followed the link[1] to the original author of the desktop software this web app is derived from, and he says: > To make a long story short, by the third generation of ReferenceFinder (written in 2003), I had incorporated all 7 of the Huzita-Justin Axioms of folding into the program, allowing it to potentially explore all possible folding sequences consisting of sequential alignments that each form a single crease in a square of paper. Of course, the family tree of such sequences grows explosively (or to be precise, exponentially); but the concomitant growth in the availability of computing horsepower has made it possible to explore a reasonable subset of that exponential family tree, and in effect, by pure brute force, find a close approximation to any arbitrary point or line within a unit square using a very small number of folds. (emphasis added) [1] https://langorigami.com/article/referencefinder/

The article talks about Robert J. Lang (https://langorigami.com), but he deserves more than a passing mention if we're talking about origami. He's a physicist/mathematician at NASA, an AMS Fellow, and also one of the top origamists in the world. Here's a video showing his extraordinary origami insects: https://www.youtube.com/watch?v=CYoTCssVyJU He wrote dozens of papers about the mathematics of origami over the years, and last year he came out with a gorgeous book on the subject: Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami (https://www.amazon.com/Twists-Tilings-Tessellations-Mathematical-Geome… He also has a bunch of origami books with "regular" animal models, but they tend to be on the complex end of the spectrum, so they're not for beginner origamists. He also developed TreeMaker, which is a software tool for systematically designing folding patterns from a model specification: https://langorigami.com/article/treemaker/ (some of his complex insect models are based on TreeMaker folding patterns)

Thanks for the link. Just a minute perusing and I'm already intrigued by a post on something that I had also observed but not thought to frame in quite the same manner: https://langorigami.com/article/optigami/

There's much more to a telescope than the primary mirror which the author conveniently neglects. As others point out below, making an IR observatory (JWST) requires keeping everything around the mirror cold so that the mirrors and instruments (not trivial, either) have a hope in heck of working. Livermore tested a multi-meter thin Fresnel optic back in 2002. They also worked with Robert Lang, physicist and origamist, to figure out how to pack the thing effectively. https://digital.library.unt.edu/ark:/67531/metadc1412512/m2/1/high_res… https://langorigami.com/article/eyeglass-telescope/

Origami is one of those subjects that hits the aesthetic button as well as the technical button .. it forms the roots of a means of manifesting "programmable matter" which is long overdue for a bit of crazy technological innovation. Every now and then I go through a phase of "catching up with the state of the origami art" and it is always rewarding to see the progress made by academics and scientists alike .. I find Computational Origami utterly fascinating, personally: https://langorigami.com/article/computational-origami/

Concept of a giant, origami space telescope using a Fresnel lens: https://langorigami.com/article/eyeglass-telescope/

Treemaker link [0] - https://langorigami.com/article/treemaker/ (missed updating the link)

There is an origami-focused, peer-reviewed academic conference "OSME" and the papers that have come out of it (released in books) are interesting reads. The conference website is http://osme.info/ (hasn't been updated in a while; see Robert Lang's page for more info: https://langorigami.com/article/origami-conferences/)

Cool links from syllabus: Origami Simulator: http://www.tsg.ne.jp/TT/software/index.html Treemaker: https://langorigami.com/article/treemaker/

Oh he's hardly a hobbyist. :) From his biography: https://langorigami.com/about-robert-j-lang/ Robert J. Lang has been an avid student of origami for over fifty years and is now recognized as one of the world’s leading masters of the art, with over 700 designs catalogued and diagrammed.

I would suggest origami. Origami is probably the art form that's been studied by mathematicians and computer scientists more than any others, e.g., flat-foldable origami crease patterns obey some simple mathematical theorems [1]. There has also been considerable research into finding an origami crease pattern for a particular target shape, and software such as TreeMaker helps one do that [2]. [1]: https://en.wikipedia.org/wiki/Mathematics_of_paper_folding#Flat_foldin… [2]: https://langorigami.com/article/treemaker/

That would be a research subject in the mathematics of origami. That field is fairly advanced (See for example http://www.langorigami.com/science/science.php), but I am not aware of people studying 'boxes'.

The posted article doesn't have examples of the copied art, but this page does: http://www.langorigami.com/copyright/sarah_morris_copyright_infringeme… It's not a matter of similarity, or independent creation - The painter Sarah Morris directly copied the original artist's work, removed the lines and colored in the voids. Since there's no question that copying took place, the case will hinge on whether the copying was "fair use" - that's where the issue of whether the copying was "transformative" comes in.

Sometimes the two meet: http://www.industrialorigami.com/technology/how.cfm http://www.langorigami.com/science/science.php4 The latter link references a variety of particular interesting applications, from airbag design to laser waveguides.