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some assistance required

PostPosted: August 20th, 2006, 8:00 pm
by hahahahiloveyou
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

PostPosted: August 20th, 2006, 9:14 pm
by Ondrej.Cibulka
First fold half, than main diagonal and then how is shown on the picture. The marked spot is in 1/3 of the paper.
Image

PostPosted: August 20th, 2006, 10:05 pm
by hahahahiloveyou
thank you soo much

PostPosted: August 21st, 2006, 9:07 am
by giro
And to divide in 5 equal parts?

thk.
Giro

PostPosted: August 21st, 2006, 10:20 am
by 4sigma
[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)}.

PostPosted: August 21st, 2006, 1:37 pm
by Daydreamer
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

PostPosted: August 22nd, 2006, 8:44 am
by Ondrej.Cibulka
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.
Image