grids and dividing angles help topic
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grids and dividing angles help topic
i have had trouble with this in the past, and decided that other people probably do likewise, so i made this. feel free if you have another link to post it in the replies, and i will add it to this is i find it fit.
dividing paper (for a grid):
3rd's:
PDF: link
Video: link
5th's:
PDF: link
Video: link
7th's:
PDF: link
Video: link
9th's:
Video: link
11th's:
Video: link
13th's:
Video: link
equilateral triangles:
link
'annoying' grid guide:
This is for the grids, like 17, 31, 13.5, stuff like that. weird numbered grids.
1. take an example grid, lets say 31, which is a prime number. therefore, the only factors are 1 and 31. find the nearest number to 31 that is not a prime number. in this case, 32.
2. fold the grid of 32. (2, 4, 8, 16, 32)
3. cut off 1 unit of 2 sides that are touching each other.
not like this: | |
but like this: |__
(of course the lines represent the edges)
Haga theorem:
introduction
further intruction
Other:
Folding angle's of 30 and 60 degrees:
link
trisecting angles:
link
quintisecting angles:
link
how to divide a square of paper (JOAS):
link
helpful progams:
Reference finder: link
dividing paper (for a grid):
3rd's:
PDF: link
Video: link
5th's:
PDF: link
Video: link
7th's:
PDF: link
Video: link
9th's:
Video: link
11th's:
Video: link
13th's:
Video: link
equilateral triangles:
link
'annoying' grid guide:
This is for the grids, like 17, 31, 13.5, stuff like that. weird numbered grids.
1. take an example grid, lets say 31, which is a prime number. therefore, the only factors are 1 and 31. find the nearest number to 31 that is not a prime number. in this case, 32.
2. fold the grid of 32. (2, 4, 8, 16, 32)
3. cut off 1 unit of 2 sides that are touching each other.
not like this: | |
but like this: |__
(of course the lines represent the edges)
Haga theorem:
introduction
further intruction
Other:
Folding angle's of 30 and 60 degrees:
link
trisecting angles:
link
quintisecting angles:
link
how to divide a square of paper (JOAS):
link
helpful progams:
Reference finder: link
Re: grids and dividing angles help topic
Thanks a lot!
All my stuff:
http://www.flickr.com/photos/55872529@N00/sets/
http://www.flickr.com/photos/55872529@N00/sets/
- Brimstone
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Re: grids and dividing angles help topic
I read Lang's quintisection method but could not understand it. Dividing the corner of a square (90°) shouldn't be that hard. Any other sources? I've searched the internet without luck.
Re: grids and dividing angles help topic
Dividing into Fifths and other uneven divisions:
http://www.origami.at/diagrams/boxpleating_guide_2.pdf
http://www.origami.at/diagrams/Fifths.pdf
http://www.origami.at/diagrams/boxpleating_guide_2.pdf
http://www.origami.at/diagrams/Fifths.pdf
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Re: grids and dividing angles help topic
Anna, those diagrams you pointed out are for dividing a side in 5ths, but what I was looking for is dividing an angle (a 90° in this case) in 5ths.
Re: grids and dividing angles help topic
What about dividing in fifths using the dichotomic method?
(This example is for a 90° angle as an answer for the previous message, but it works for each and every angles).
- Fold an estimate of 2/5 of your angle, crease lightly (crease #1), unfold. Comparison between this poor estimation and the real 2/5.
- Fold this roughly 2/5 in half (i.e., bring the bottom edge of your paper to crease #1) and crease lightly (crease #2), unfold.
- Fold the opposite edge of your paper to crease #2, hence folding a rough 2/5 from the other side (crease #3), unfold.
- Fold the edge you just used to crease #3, which is your last rough 1/5 (crease #4), unfold.
- Now fold the bottom edge of the paper to crease #4, beginning next iteration.
- Repeat all three remaining steps, creasing sharply now because the error from the first fold has been really minimised (any mathematics lover could probably tell by how much this method reduces the error per iteration). Here are the second iteration folds, in blue (notice how #4 and #4 next iteration are very close even though #1 was not so precise).
[edit] Added picture links. [/edit]
(This example is for a 90° angle as an answer for the previous message, but it works for each and every angles).
- Fold an estimate of 2/5 of your angle, crease lightly (crease #1), unfold. Comparison between this poor estimation and the real 2/5.
- Fold this roughly 2/5 in half (i.e., bring the bottom edge of your paper to crease #1) and crease lightly (crease #2), unfold.
- Fold the opposite edge of your paper to crease #2, hence folding a rough 2/5 from the other side (crease #3), unfold.
- Fold the edge you just used to crease #3, which is your last rough 1/5 (crease #4), unfold.
- Now fold the bottom edge of the paper to crease #4, beginning next iteration.
- Repeat all three remaining steps, creasing sharply now because the error from the first fold has been really minimised (any mathematics lover could probably tell by how much this method reduces the error per iteration). Here are the second iteration folds, in blue (notice how #4 and #4 next iteration are very close even though #1 was not so precise).
[edit] Added picture links. [/edit]
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Re: grids and dividing angles help topic
If I have to x-sect an angle (which is rare for me), I just eyeball it. That's the easiest method, but you can only get better with experience.
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Re: grids and dividing angles help topic
@Kabuntan:
Thanks for the instructions and images.
Thanks for the instructions and images.
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Re: grids and dividing angles help topic
Great links, everyone!
Does anyone know any links where you can divide a paper into 15? I know the 'annoying grid' guide but I hate to cut the paper and reduce it's size. So if anyone has a direct way to divide into 15, please share.
Does anyone know any links where you can divide a paper into 15? I know the 'annoying grid' guide but I hate to cut the paper and reduce it's size. So if anyone has a direct way to divide into 15, please share.
Re: grids and dividing angles help topic
You can either fold fifths and divide them into thirds or vice versa.
Or you could use the Haga theorem (http://www.origami.gr.jp/Archives/Peopl ... /06-e.html) to get for example 7/15 to 8/15.
Or you could fold an equally sized sheet into 16th and use it as a guide, by placing your new sheet over the sheet with the 16th, making sure that lets say the lower left corners touch. Then shift the upper left corner so that it touches the 15th grid line. Now you can use the grid below as guide to show you where the fold lines need to be.
Or you could use the Haga theorem (http://www.origami.gr.jp/Archives/Peopl ... /06-e.html) to get for example 7/15 to 8/15.
Or you could fold an equally sized sheet into 16th and use it as a guide, by placing your new sheet over the sheet with the 16th, making sure that lets say the lower left corners touch. Then shift the upper left corner so that it touches the 15th grid line. Now you can use the grid below as guide to show you where the fold lines need to be.
Re: grids and dividing angles help topic
I think this link has already been posted: http://www.giladorigami.com/Articles_Divisions.html , similar to what Anna has posted, but it's worth looking at all the links to try to follow the math behind folding divisions.
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Re: grids and dividing angles help topic
Thank you, both.
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Re: grids and dividing angles help topic
the easiest, cleanest, and most accurate way to get abnormal grid divisions is as follows
step one- divide the base of your divisions by two (e.g.- if you want 29ths, divide 29 by 2 which would be 14.5)
step two- round up that number to the nearest power of 2 (1,2,4,8,16,32,64 etc.) (14.5 rounded up to the nearest power of 2 would be 16)
step 3- subtract your power of 2 from your original number (29 is our original number, so 29-16=13)
step 4- create a fraction by making the number from the previous step your numerator and the power of 2 the denominator (for this example, that would be 13/16)
step 5- create a crease line on the edge of your square of that fraction (in this case, divide the paper into 16ths, which you should know how to do, but only make a hard crease on the division 13/16ths.)
step 6- connect that crease to the corner of your square with another straight crease line
7- crease the diagonals of the square
8- the point at which your crease from step 6 and the diagonal of your square will divide the diagonal of the square into your needed division (in this example, it would divide the diagonal so that the shorter side will be 13 units long, and the longer will be 16 units long. 13+16=29)
its hard to explain correctly, but once you get the concept of it, it'll be very easy for you to create any sort of grid
step one- divide the base of your divisions by two (e.g.- if you want 29ths, divide 29 by 2 which would be 14.5)
step two- round up that number to the nearest power of 2 (1,2,4,8,16,32,64 etc.) (14.5 rounded up to the nearest power of 2 would be 16)
step 3- subtract your power of 2 from your original number (29 is our original number, so 29-16=13)
step 4- create a fraction by making the number from the previous step your numerator and the power of 2 the denominator (for this example, that would be 13/16)
step 5- create a crease line on the edge of your square of that fraction (in this case, divide the paper into 16ths, which you should know how to do, but only make a hard crease on the division 13/16ths.)
step 6- connect that crease to the corner of your square with another straight crease line
7- crease the diagonals of the square
8- the point at which your crease from step 6 and the diagonal of your square will divide the diagonal of the square into your needed division (in this example, it would divide the diagonal so that the shorter side will be 13 units long, and the longer will be 16 units long. 13+16=29)
its hard to explain correctly, but once you get the concept of it, it'll be very easy for you to create any sort of grid