What is the best way to divide a square piece of origami paper into 17 parts?
Todd
Dividing a square piece of origami into 17 parts
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 Brimstone
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Re: Dividing a square piece of origami into 17 parts
Divide each side into 18 ths and cut off one strip on two edges.
Dividing into 18ths is done by dividing into 3rds, then each 3rd into 3rds again and then dividing those 9ths in half.
Dividing into 18ths is done by dividing into 3rds, then each 3rd into 3rds again and then dividing those 9ths in half.
Re: Dividing a square piece of origami into 17 parts
Crossing diagonals! Precrease the top and right edges into fourths, and make a crease from the bottom left corner to the first fourth up the right side.
In the same way, make a crease from the bottom right corner to the fourth on the top closest to the right side.
The intersection of these diagonals will be (16,4).
In the same way, make a crease from the bottom right corner to the fourth on the top closest to the right side.
The intersection of these diagonals will be (16,4).
 Brimstone
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Re: Dividing a square piece of origami into 17 parts
Tankoda, could you please elaborate on your answer? I did not understand what you meant, what would be the use of (16,4)?
Re: Dividing a square piece of origami into 17 parts
I'm not sure if that is what Tankoda ment, but it should work as well:
The left bottom corner zoomed in:
By the way, this works for other odd divisons as well. E.g to go from 1/4 > 1/5 or from 1/8 > 1/9...
The left bottom corner zoomed in:
By the way, this works for other odd divisons as well. E.g to go from 1/4 > 1/5 or from 1/8 > 1/9...
splunge.de  Origami, Papercraft, Scale models, Photography
Re: Dividing a square piece of origami into 17 parts
WOW... I had NO idea about this, and I like it a lot more than Brimstone's solution of cutting the paper after folding .
Thank you Tankoda and Splunge!

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Re: Dividing a square piece of origami into 17 parts
I second Tankoda's method.
Splunge's method would work in theory, but it's really difficult in practice. A diagonal of rectangle with anything more than about a 6:1 aspect ratio is really tricky to fold cleanly at the corner.
Gerardo, it works for irrational divisions as well. You can theoretically use that method for any realnumber ratio you want; the only limit is the difficulty of constructing the numbers.
Splunge's method would work in theory, but it's really difficult in practice. A diagonal of rectangle with anything more than about a 6:1 aspect ratio is really tricky to fold cleanly at the corner.
Gerardo, it works for irrational divisions as well. You can theoretically use that method for any realnumber ratio you want; the only limit is the difficulty of constructing the numbers.