During her mathematical studies, Elina Gor researched the changes in complexity of origami models from the 1980`s to the present, to see if we are doomed to face mega-complex models in the future or maybe we already have reached the peak of complexity.
Diagrams for a color-change modular, 12 or 30 units, though like most polyhedral designs, the latter is more attractive. The flower petals are of one color, and the flower centers and background are of another color.
In origami we frequently need to find an \(n\)th of a paper, often in order to divide it into an \(n \times n\) grid. This article generalizes a common technique for finding references and provides some insight into the geometric properties of paper.
The 3-unit Sonobe hexahedron (Toshie's Jewel) and the 12-unit Sonobe octahedral assembly are well known Sonobe constructions. But did you know that you can also construct the former with double the number of units, and the latter with half the number of units, i.e., both shapes from 6 units?
Diagrams for the solid version of the Compound of 5 Tetrahedra aka the 47th Stellation of the Icosahedron, similar to the very popular frame version by Tom Hull/Francis Ow, known as Five Intersecting Tetrahedra or FIT. Some mathematics has been discussed as well.
A quick and easy method of folding a heptagon by Jacques Justin and some related discussions. Francesco Mancini found the method in a pile of letters and notes that he inherited from Roberto Morassi's origami archive.
Tridecagon, also known as the triskaidecagon, is a 13-sided polygon. There are several origami methods already available for folding the tridecagon but the simplicity of my approach may be of interest to people. You may use the tridecagon to transpose origami designs based on other regular polygons.
Toyoaki Kawai’s method of making a pentagon from a square is a widely used one. This article demonstrates how to extend his method to a decagon and shows examples of transpositions of well known designs to pentagons and decagons.
Curved-crease origami can be designed by considering the properties of ruling lines, lines on the crease pattern that remain straight in the 3D folded form. This technique was developed by David Huffman, who identified conic section curves has being particularly suitable for curved-crease designs. Two examples using ellipses are given as crease patterns.
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.
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!
An expanded version of a 5OSME convention commentary that appears in the Winter 2011 issue of The Paper, pp 18-19. Many more interesting experiences and color photos that could not be included in The Paper version due to limited space.
The origami wind spinner is a traditional, if somewhat obscure model of repeated pleat folds. We ask ourselves, "What kind of shapes can paper form with these simple pleats?" and, "How much can we make a square piece of paper rotate with this pleating scheme?" The answers are surprising and fun!