My workshop in Purranque: The Kawasaki Rose

A classic figure in origami is the rose created by Toshikazu Kawasaki from his famous twist folding. Its delicate curve petals had made it one of the most popular and spread models inside origami (and outside).

History of this rose is easier to build than the one of its author. There is very few about this japanese mathematician, who teachs in the Sasebo Technologycal School and became the first "Doctor in Origami" of History. He is also known for his theoretical studies about the relationship between origami and mathematics, developing, among others, the Theory of Iso-Areas (Mirror Areas). In 1998 he pulished Roses, Origami & Math (which should be now on its way to my home :) )

On this book there is a complete chapter dedicated to this rose and its variations, being this the first version "from the author" of its diagram. Before, in 1994, during the New York Convention, Kawasaki teached the rose to the american creator Joseph Wu and he folded and gifted one to his friend Winson Chan. He unfolded the gift and developed a folding sequence and diagram, which was published and spread trough the net, becoming very popular and known as the "New Kawasaky Rose". Later, japanese Kunihiko Kasahara published in his book "Origami for the Connoisseur" a diagram a little less elaborated than Chan's and called it the "Original Kawasakai Rose". Many other variations has been created over this three diagrams, to get a larger number of petals or diferents finishing details, but the heart of this figure, the twisting fold, remains unvariable as a testimony of the geniality of its author.

Chan's diagram remains being my favourite, mostly because its final result and also I guess because sentimental reasons (it was one of the first figures I've memorized and gifted) However, I have to admit that its 22.5º grid pre-folded takes out all ellegance to the next steps in the folding. Here there is a video about how the rose is collapsed from its pre-folded CP.

It is precisely the analysis of the New Rose what gave the folder a deep learning about the relationship between geometry and origami. To build this rose is almost being creating, step by step, the CP of the figure, to collapse it then in a couple of master moves. The point I want to remark is that anyone who has folded this a couple of times can realize that the pre-folding of the grid is unnecessary to get tits main folds (step 12 of Chan's diagram). The perfect geometry of Kawasaki give us a large number of references to achieve every one of them from two simple diagonal lines at 22.5º. This is especially useful when you use thick papers o textured to fold the rose, because Chan's method to draw the grid lose accuracy over the edges.

With this in mind, and studying a little, I could develop a diagram to get the full figure from a couple of reference lines, including the secondary petals from steps 9 to 11 on Chan's diagram.

For example, to generate folds from Chan's step 12, it is only necessary the axial line and a reference point, aligning the line over itself and marking the fold passing through the reference point, as I show in the next image:

Is when I remember my old Maths teacher at school, saying by memory: "there is one and just one perpendicular line to a given line which passes through a given point". That can be read as an Origami Theorem: "To fold a perpendicular line of a given one is necessary only that line and a given point"

There are also other references to follow in this particular fold, as I show them in the image above.

Same thing occurs with the other folds from that step:

My hope was to get the rose whit the less possible number of foldings, to get the petals as much clean as possible, but at the end, just a few of them can be avoided. Also the sequence itself is as complicated as Chan's (or even more). All I could keep was the great experience of having learned a lot and grown-up in my relationship with folding and geometry, both things which justify the experience and that's why I share it to anyone who desires to try it. This is the link to the document Google Base page and thi is the direct link to the document (it is zip pdf file and its size is about 1 Mb):

newrose2.pdf.zip

Many regards and luck if you try it :), I'll be happy to answer any question about it.