Dollar Bill Rosettes by Paul Jackson and Martin Kruskal (first hour)
In this session, we will fold the original Dollar Bill Rosette, with 16 panels. Paul taught the model to Martin and Laura Kruskal. Martin then designed a model with 22 panels. A follow-on session will reveal [some of] the mathematics.
Mathematics of the Martin Kruskal Dollar Bill Rosette (second hour)
Lecture: no folding - you may skip the first hour and join in for the lecture if you already know the model
Martin Kruskal's Dollar Bill Rosette (22 panels) starts with estimating 1/11 of an edge. The folding procedure starts with an estimate and marks off the 10 points dividing the edge. In doing this, the estimate is improved by halving the amount of error at each fold. In this talk, I will show the algebraic proof of how this is done. It is similar to a technique used for dividing an edge into thirds. I also will prove that the numbers for which the folding procedure works, that is, hit all the intermediate points, is the same as the Reptend Primes Base 2. The work is my own. I am confident that Martin Kruskal knew all about this.
Skill level: high school algebra or the willingness to listen and realize that your fingers do considerable mathematics when folding.
The Kruskal model is described in our book, written with Takashi Mukoda, More Origami with Explanations.
Dollar bill or similar paper currency or paper substitute. Please avoid the UK or Canadian currency with plastic inserts. You also can use paper rectangles. 2.61 x 6.14. It does not have to be exact.