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Wednesday, 20 January 2010

Origami & Patents


How many philanthropists have raised money for charity by making and selling origami? Fifth grader Sebastian Carpenter, only 11 years old, did just that, raising USD$610 for a local charity in Massachusetts. Sebastian created and sold Christmas-themed origami to family friends, hoping to raise only $50. As word about his cause and his creations spread, demand for the origami pieces rose, eventually selling 60 pieces, and raising $610 for a worthy cause. (Source: Wicked Local, 13th Jan 2010. Student joins fundraising fold: Origami creations raise money for Acord Food Pantry.)

Even engineers are passionate about origami. In December 2009, Japanese aeronautical engineer, Takuo Toda, created a world record for creating a paper plane that stayed airborne for 26.1 seconds, while staying true to the rules of origami: no scissors, and no glue. Takuo previously made the world record for creating a paper plane that stayed airborne for 27.9 seconds, but had deviated from origami rules by using cellophane tape. He plans to exceed 30 seconds on his next attempt. (Source: The Guardian, 27 Dec 2009. Paper plane enthusiast sets flight record.)


The recreational art of paper folding originated from Japan. The word "origami" comes from Japanese words "oru" (which means "to fold") and "kami" (which means "paper"). The recreational art of paper folding became popularly known as "origami" at the end of the nineteenth century, or the early twentieth century. Before that, it was known as "orikata", "orisue", "orimono", "tatamgami", among others, which also referred to origami. (Ref:, Origami History. Accessed: 20-1-2010.)

Flying cranes usually come to mind when we hear the word "origami". Origami as an art form is versatile, beautiful, useful, and is more than just flying cranes. Consider:
  1. Origami has been found to be tremendously helpful to the area of engineering. (Ref: Web-Japan, 12th Mar 2008. The Science of Origami.)
  2. Rigid origami is studied as the science of "folding structures using flat rigid sheets joined by hinges", and is considered a type of mechanical linkage. (Ref: Wikipedia)
  3. Fresnel lenses have been packed on Earth using origami techniques and unpacked in outer space. (Ref: California Connected. Interactive: An Origami Space Telescope.)
  4. Various architectural structures utilize principles from origami. (Ref: Pleated Structures)
  5. Origami based furniture -- made of aluminum and cardboard -- has proven to be usable and viable. (Ref: Origami Resource Center, Origami Furniture.)
  6. Orikaso, founded by Tomoko Fuse sells flat, foldable polypropylene tableware that transform from flat sheets into cups, bowls and plates. Orikaso claims that polypropylene is the only alternative to PVC endorsed by Greenpeace. (Found via Origami Resource Center, Origami Furniture.)

The Orikaso flat foldable tableware series
The following videos show:

(i) A blue plate.

(ii) A green cup.

(iii) A red bowl.

Orikaso's products are patented as US patents #6,237,845 and #6,595,409. They are assigned to Kuramae Sangyo Co., Ltd. of Japan.

US Patent #6,237,845

US Patent #6,595,409

Beautiful Tessellations

Eric Gjerde runs a site, featuring printable origami "crease patterns" (CP). Origami tessellations can be quite beautiful to look at. Eric Gjerde has written a book, Origami Tessellations: Awe-inspiring Geometric Designs, which you can browse below.

You can view more beautiful origami tessellations at the Origami Tessellations Flickr group.

Miura-Ori Folding

Miura-Ori origami is a relatively recent development in origami. It looks quite similar to herringbone pleating. Ed Cavett, an artist from Illinois, folds, frames and sells Miura-Ori origami as "wall art". A description of Miura-Ori at his website:
The Miura-Ori origami fold is a class of concave polyhedral surfaces of varying degrees of corrugation (Miura, Koryo, 2006). The folds involve reciprocating parallelograms protruding into the z-plane.

As the depth of the protrusion increases, the width of the sheet decreases while the length remains the same.
(Ref: Cavett, E. (2008). About the Miura-Ori origami pattern. In Wall Art, Ed Cavett Studio Web site.)

In October 1980, New Scientist carried a story about how Miura and Sakamaki created a new method of folding maps at 84' to produce congruent parallelograms, which reduced tears caused by conventional orthogonal folding.
Miura and Sakamaki ... came to the conclusion that the most important point of difference from an orthogonally folded sheet is that the folds are interdependent. Thus a movement along one fold lire produces movement along the other. In other words, the user can open the map with just one pull at a corner.
(Ref: New Scientist, 23rd Oct 1980. The Miura-Ori Map. Reproduced in The British Origami Society website.)

The Miura-Ori folding technique can be seen from this simple video.

And the Miura-Ori map folding-unfolding action can be seen in this video.

Here are some links about Miura-Ori folding:
  1. Wikipedia's entry on Miura-fold.
  2. Japan Aerospace Exploration Agency (JAXA) has pictures showing a Japanese space shuttle employing the Miura-Ori folding technique to pack and unpack a solar panel. (JAXA, No.4 宇宙に開く「ミウラ折り」. Link found via Origami Science Centre website; page on Origami Science.)
  3. Graphical instructions, scanned from a magazine, demonstrate how the Miura-Ori folding technique folds maps both horizontally and vertically, simultaneously. (Ref: ThinkQuest, Miura-Ori folded by Square root of 2 Rectangle. Accessed: 20-1-2010. Scanned from monthly magazine "Origami" NO.194 by Nippon Origami Association.)
  4. A paper by Pellegrino and Vincent, "How to Fold A Membrane", discusses how a membrane can be folded like a letter, and, after discussing the Miura-Ori folding technique, how a membrane can be folded in a rotational manner around a central hub. (Ref: S. Pellegrino and J Vincent, How to Fold a Membrane. Hosted at University of Bath.)
  5. In October 2006, the "Japanesque Modern" committee awarded the J-Mark award to 53 products and systems which "fuse Japanese traditional cultures, materials, techniques and spirits with cutting-edge technologies". One of the winners is the Miura-Ori map folding technique, "also deployed for solar panel arrays on satellites." (Ref: Tech-On newsletter, 31st Oct 2006. Published online by Nikkei Electronics Asia. 'Japanesque Modern' Selects 53 Products, Contents Representing 'Japaneseness'.)
  6. In March 1971, an article by Miura and Sakamaki in a journal of the Institute of Space and Aeronautical Science, University of Tokyo, discussed "buckle pattern tessellation" on a cylindrical surface; or, more plainly, the repetitive pattern of folds that results when a cylinder collapses from being compressed at both ends. Miura and Sakamaki were concerned with cylinders of various curves, including elliptical cylinders. (Ref: Institute of Space and Aeronautical Science, University of Tokyo, Report No 461, March 1971. Koryo Miura and Masamori Sakamaki. Discontinuity of Buckle Pattern Tessellation of Cylindrical Shells of Variable Curvature. Provided by Japan Aerospace Exploration Agency.)
  7. To understand the "buckle pattern tessellation" on cylindrical surfaces, view pictures of diamond pleating.
  8. A blog, Meme Queue discusses various map folding techniques. Note the references to Patent Support Mates and Compass Maps.(Ref: Meme Queue, 19th Feb 2009. The Easiest Way To Refold A Map.)

In Japan, Patent Support Mates Co., Ltd., patented a cost-saving production method for maps using the Miura-Ori folding technique, and also registered trademarks and designs. (Ref:, Intellectual Properties.) It is not clear if the company is linked to Koryo Miura.

Interested readers can read "The Science of Miura-Ori", by Koryo Miura. The abstract is here. The actual article is below. (Ref: "The Science of Miura-Ori: A Review", a chapter in the book Origami 4, available at Google Books.)


The Miura-Ori folding technique has been cited in several US Patents.

US Patent #6,644,694: A wearable map.

US Patent #7,281,556: Pneumatic tire with tread portion having zigzag sipes

US Patent #7,334,619: Pneumatic tire with blocks having zigzag sipes

US Patent #7,060,292: Deployable stent

US Patent Application #11/483,328: Folding structures made of thick hinged sheets

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