These are two articles I have written about the how I use Geometer's Sketchpad, a program intended to teach high school geometry, to precisely build my crease patterns. More specifically, they detail how I calculate and construct the circle packing - they do not go into the theories and methods for how to circle pack or how to fill in the creases for the resulting molecules. Those topics are covered in great detail in Robert Lang's book Origami Design Secrets.
This article represents a math problem that I solved regarding the packing of concentric rings of circles while keeping them perfectly tangent. It only applies to how I used to design flowers and does not represent the way I approach constructing any designs other than the ones specifically mentioned in the article. I now find box pleating more conducive to creating rings of flaps on a square paper without wasting space.
This article represents the way I have continued to construct any of my circle packed designs since I wrote it in 2009. It allows me to geometrically construct the circles so that they are perfectly tangent to each other and are based on a set of underlying flap lengths. This allows for far greater accuracy than arranging them by hand, and it also lets me make small adjustments to the lengths without the need to move all the circles by hand again - they automatically remain tangent to each other.
