Iris Folding Computer Design
By far, the easiest way to create your own iris folding pattern is to use a pencil and a ruler and draw concentric shapes each smaller than the previous. But if you are one of those people who like to draw on a computer, you will need a way to calculate two things:
1) the size of the inner square
2) the angle to rotate the inner square.
The equations below will allow you to calculate the size of the inner shape and the angle of rotation. Armed with that info, you can generate the inner shapes and rotate them so they fit into a nice spiral. Two solutions are provided: the first is for a square and the second is suitable for other shapes such as a triangle, pentagon, hexagon, and so forth.
Calculations for a Square Template
You want to determine length of side C and angle of rotation a.
The side lenght of the inner square can be determined with Pythagoras’ theorem:
a^{2} = b^{2} + c^{2}
You would think that if you start with a square of size 3″ and you decrease its size by 0.5″ then the inner square would be 2.5″. This is not true because you are rotating the inner square so the size needs to be a little large that expected.
The angle of rotation can be determined with the trigonometry tanφ = y/x
Summary
Start with first square of size 3 inch.
Make second square size 2.55 inch, rotate it 11.3 degreees.
Repeat calculation with L = 2.25 and K = 0.5
Continue until inner most square is close to or less than 0.5 inches wide
Calculations for Triangle, Pentagon, Hexagon, and More
Shape  Angle c 
triangle  60 degrees 
square  90 degrees 
pentagon  108 degrees 
hexagon  120 degrees 
heptagon  128.57 degrees 
octagon  135 degrees 
nonagon  140 degrees 
The side length of the inner triangle can be determined with the law of cosines:
a^{2} = b^{2} + c^{2} – 2abcos(c)
Note that angle c is 90 degrees for a square, so cos(90) = 0; this means the 2abcos(c) part becomes zero and the equation reduces to a^{2} = b^{2} + c^{2} which is the same as the instructions above for a square. [The law of cosines reduces to the pythagorean theorem for right triangles.]
Remember that cos(c) is
cos(60) for triangle
cos(90) for square
cos(108) for pentagon
cos(120) for hexagon
cos(128.57) for heptagon
cos(135) for octagon
cos(140) = nonagon
The angle of rotation can be determined with the law of sines where:
A = B = C
sin(a) sin(b) sin(c)
Again, remember that sin(c) is different depending on the shape you are working with:
sin(60) for triangle
sin(90) for square
sin(108) for pentagon
sin(120) for hexagon
sin(128.57) for heptagon
sin(135) for octagon
sin(140) = nonagon
Books about Iris Folding
 Iris Folding Stylish Greeting Cards by M. Gaasenbeek
 130 New Iris Folded Cards to Make by M. Gaasenbeek
 Iris Folding 2: 29 Designs for Cards and Scrapbooks by C. Donasky
 The Simplicity of Iris Folding by Sarah Decker
 Iris Folding For Winter by Gaasenbeek & Beauveser
 see Iris Folding books
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