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Postby hahahahiloveyou » August 20th, 2006, 8:00 pm

hello,
i have recently become interested in folding my own modular 60 degree unit bu francis ow and saw that you must have sheets of 1x3 paper so my question is..

is there any trick to fold a peice of 1x1 paper into 3 equal parts w/o much guess work?

thanks in advance
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Postby Ondrej.Cibulka » August 20th, 2006, 9:14 pm

First fold half, than main diagonal and then how is shown on the picture. The marked spot is in 1/3 of the paper.
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Postby hahahahiloveyou » August 20th, 2006, 10:05 pm

thank you soo much
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Postby giro » August 21st, 2006, 9:07 am

And to divide in 5 equal parts?

thk.
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Postby 4sigma » August 21st, 2006, 10:20 am

[img]http://img301.imageshack.us/img301/4923/fifthvb9.png[/img]

In general, you can divide the paper into N+1 parts by:

1) Dividing it into N parts along the left edge
2) Making a crease from the bottom right corner to a distance 1/N up the left edge
3) Making the diagonal crease from the bottom left to the top right.
4) The point where these two creases intersect is a distance of 1/(N+1) from both the left and bottom edges.

Algebraicaly you can prove this because the creases form the lines y=x and y= (1 - x)/N. These intersect at the point {1/(N+1), 1/(N+1)}.
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Postby Daydreamer » August 21st, 2006, 1:37 pm

For general divisions this page about the Haga theorems might be interesting to you as well:
http://www.origami.gr.jp/People/CAGE_/divide/index-e.html
So long and keep folding ^_^
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Postby Ondrej.Cibulka » August 22nd, 2006, 8:44 am

Theorems are nice, but how to make 1/5? Try to look in Origami for the Connoisseur...
At first fold in half, than one corner as shown. The 1/5 is at the marked point and red line.
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