# Math & Science Posts

Below are the latest posts on this site that I’ve written on various topics in math and science. Click the subject listings to the right to see other posts in other categories (both science and general).

I also have some book, magazine, and journal publications in math and science: see journal articles here, my books here, and a listing of all external publications here.

#### Computational Origami

This page contains links to computational tools useful for origami design and for combining origami with mathematical or scientific applications. See here for additional links about origami math, science, and technology. See here for additional links not specifically related to mathematical and scientific origami. If you’ve got a computational origami tool you’d like listed, send […]

Continue Reading#### Polypolyhedra in Origami

These images show what the (first) 54 polypolyhedra would look like if created using the Ooh and Ow unit joints (Ow being Francis Ow’s mechanism for joining struts at angles up to 90 degrees, Ooh being my own similar mechanism for larger angles). Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. […]

Continue Reading#### Polypolyhedra in Dowels

These images show what the (first) 54 polypolyhedra would look like if created using round dowels of the maximum possible diameter. Polypolyhedron 1. Polypolyhedron 2. Polypolyhedron 3. Polypolyhedron 4. Polypolyhedron 5. Polypolyhedron 6. Polypolyhedron 7. Polypolyhedron 8. Polypolyhedron 9. Polypolyhedron 10. Polypolyhedron 11. Polypolyhedron 12. Polypolyhedron 13. Polypolyhedron 14. Polypolyhedron 15. Polypolyhedron 16. Polypolyhedron 17. […]

Continue Reading#### Polypolyhedra

Background In 1999, I became interested in a family of origami modulars composed of interwoven polygonal frames and/or polyhedral skeletons, the most famous of which was devised by Tom Hull, which he titled Five Intersecting Tetrahedra, now commonly known by its abbreviation, FIT. (See here for a description.) The underlying polyhedron—a compound of five tetrahedra […]

Continue Reading#### Science Links

This page contains various and sundry links to web pages that combine origami with mathematical or scientific applications. See here for links related to computational origami (software for origami design and analysis). See here for additional links not specifically related to mathematical and scientific origami. Please let me know if you find any broken links […]

Continue Reading#### Optigami

In the design of optical systems that incorporate multiple reflections of converging and diverging beams, tedious graphic layout procedures are followed to assure that mirror dimensions are correct and that structural elements do not interfere with the ray bundles. A change in dimension, location, or angle of any one of the system elements requires a […]

Continue Reading#### Eyeglass Telescope

Photograph of the Eyeglass prototype on its test range at Lawrence Livermore National Laboratory, Livermore, California. Image courtesy Rod Hyde, LLNL. Picture the solar system’s largest telescope, a telescope as long as the island of Manhattan, incorporating a lens the size of a football field: an instrument possessing the resolution to examine earth-like planets around […]

Continue Reading#### Airbag Folding

What could origami possibly have to do with automotive airbags? Quite a lot, it turns out. Sorry, your browser doesn’t support embedded videos. Animation of an airbag deployment for which the mesh was generated using an origami design algorithm. The origami creases appear in the flattening you see in the first seconds of the animation. […]

Continue Reading#### Origami Conferences

Since 1989, there have been several highly successful international scientific conferences exploring the interactions between origami, mathematics, science, and (since 2001) education. The conferences take place at irregular intervals—basically, whenever a general chair and sponsoring organization decide that the time has come for the next. Beginning in 2015, the OSME series of conferences is guided […]

Continue Reading#### 4OSME

2006-10-16 Update: 4OSME was a rousing success! Over 165 people attended some 70 talks. The 4OSME proceedings has been published by A K Peters, Ltd (now part of CRC Press). Several media groups covered 4OSME. See photographs and a trailer from Green Fuse Films’ Peabody-award-winning documentary on origami (portions of which were filmed at 4OSME), […]

Continue Reading#### Angle Quintisection

This figure shows the key step in performing an origami angle quintisection—division into equal fifths—by folding alone. Within the mathematical theory of origami geometric constructions, the seven Huzita-Justin axioms define what is possible to construct by making sequential single creases formed by aligning combinations of points and lines. It has been mathematically proven that there […]

Continue Reading#### Huzita-Justin Axioms

At the First International Meeting of Origami Science and Technology, Humiaki Huzita and Benedetto Scimemi presented a series of papers, in one of which they identified six distinctly different ways one could create a single crease by aligning one or more combinations of points and lines (i.e., existing creases) on a sheet of paper. Those […]

Continue Reading#### OrigamiUSA’s The Fold

Starting in November, 2010, I began writing a regular column on crease patterns (with occasional forays into other topics) for OrigamiUSA’s then-new online publication, The Fold. You’ll need to be a member of OrigamiUSA to read the articles, but in my highly biased opinion, it’s well worth the cost (not just for my articles, but […]

Continue Reading#### TreeMaker

Background In 1989, I wrote an article for the magazine Engineering & Science about the state of technical folding, which, even then, seemed to be progressing by leaps and bounds due to an infusion of scientific and mathematical principles. In recounting some of the connections between origami, math, and technology, I wrote: Computing succumbed to […]

Continue Reading#### Tessellatica

This page contains the current release of Tessellatica, a Mathematica notebook for the design and analysis of origami with particular emphasis on origami tessellations. You’ll need a current version of Mathematica to use it. Beginning with Tessellatica 11.x, the version numbering matches that of the version of Mathematica that it is tuned for. Specifically, the […]

Continue Reading#### Origami Simulation

Background In the 1980s, I made the acquaintance of Jacobo (Jack) Fastag, a graduate student like myself who was interested in exploring the interactions between computers and origami. We both had hit upon the idea of exploring the ability to simulate origami folding on a computer, and each set out to write our own origami […]

Continue Reading#### ReferenceFinder

Background During the development of technical folding that began in the 1980s, a new problem arose for the origami designer: how to find the major creases in the base by folding alone. This didn’t used to be a problem. In the traditional “trial-and-error” approach to origami composition, the design was discovered via exploration of folding. […]

Continue Reading#### Tessellatica and Web-Love from Wolfram

Wolfram gives me some web-ness: Above the Fold: Mathematica Transforms Ancient Art of Origami By coincidence, today I also learned that my 6OSME paper on Tessellatica was accepted (along with some others). So come to Tokyo in August, 2014 to get your free copy! (*) (*) Actually, you’ll be able to get a free copy […]

Continue Reading#### Drupalizing

One of my side activities is managing the website of OrigamiUSA, which is based on the Drupal content management system. Earlier this year, we upgraded the site from Drupal 6 to Drupal 7, a process that was not lacking in adventures. At our local Tri-Valley Drupal Users Group meeting, I presented “Lessons Learned in a […]

Continue Reading#### So That’s What’s Inside

The traditional Japanese origami crane is such an unusual shape, it makes one wonder why whoever first folded decided on calling it a crane, and also, why they gave it that particular shape. Well, now we know the answer: it’s shaped that way because that’s its skeleton, as the photo below shows. This fantastic model […]

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