These are articles posted by The Fold editor thomas.hull (who may or may not be the author; see byline for authorship). The Fold is the online magazine for members of OrigamiUSA. New articles are posted continuously over the two month period of each issue. To contribute to The Fold or for other questions, please see our FAQ.

### Diagrams: Fractal Pyramid

by Ushio Ikegami
This is the only diagrammed origami model that simulates a true mathematical fractal. It makes a pyramid shape with many branches. No one has yet successfully folded a version without cutting the paper; the version in the picture (folded by the author) was made by carefully cutting the crease pattern into several pieces, folding these using the recursive folding instructions, and then gluing them back together. The challenge of folding recursive diagrams as well as the dexterity involved to not destroy the paper easily put this model in the supercomplex category.

### Crease Pattern: Octagonal Iso-Area Self-Similar Flower

A fun crease pattern that can repeat infinitely to the center folds an octagon into a geometric flower design, where the front and back of the paper look the same.

### Book Review: Learning Mathematics with Origami

by Charlene Morrow
OrigamiUSA Board member and educator Charlene Morrow reviews a book by Tung Ken Lam and Sue Pope, two experienced British teachers of origami and mathematics.

### Cool Iso-area Hexagon Collapses

by Thomas Hull
Several variations on a hexagon-based, iso-area, geometric collapse method are shown. Some of these were taught at the 2013 OrigamiUSA Annual Convention in New York City.

### Convention: BOS Autumn 2012, Liverpool, UK

Thomas Hull
Tom Hull describes the 2012 Autumn convention of the British Origami Society, which took place on Sept. 7-9 in Liverpool, UK.

### Five Intersecting Octahedra

Meenakshi Mukerji
30 pieces of paper are folded to make a modular version of the Compound of Five Octahedra model.

### Folding Waves, Part 1

Thomas Hull
This wave model is fun to fold and has a lot of math in it!

### Spotlight: Margherita Beloch

by Tom Hull
Learn some of the history of origami geometry, as well as the story of Margherita Liazzolla Beloch, the first origami mathematician!

### How to Prove that Origami is Hard

by Tom Hull
A summary of Bern & Hayes' proof that flat-foldability in origami is computationally hard!

### Divider Inserts for N-sided Boxes

by Arnold Tubis and Crystal E. Mills
A method for making four-compartment side–to–side or corner–to–corner divider inserts for prism-shape containers with square faces is generalized so as to produce n equal compartments of specified height for a container with an n–sided regular-polygon face.

### Crease Pattern: Honeycomb

With many tessellations, the obvious way to design the crease pattern doesn't necessarily result in a foldable pattern. By adding extra creases to the pattern, you can sometimes find an alternate way to the finished form, as you'll see in this geometric pattern.

### The Theorems of Maekawa, Kawasaki, and Justin

Thomas Hull
The names Maekawa and Kawasaki are known to origamists as great origami creators. But did you know they have Theorems named after them too? And so does the French paper folder Jacques Justin. See what these Theorems are all about. Warning: Math ahead!

### Origami & Calculus

Tom Hull
Every time you fold paper, your fingers are doing calculus. Read more to learn how smart your fingers are!