Hi. Can you please show me how can I mathematically reach the measurment of x in the fish base of the following image, when I know the measurement of y?
Thank you in advance .
How to reach the measurement of this crease on a fish base?
Forum rules
READ: The Origami Forum Rules & Regulations
READ: The Origami Forum Rules & Regulations

 Moderator
 Posts: 2328
 Joined: December 25th, 2011, 7:15 pm
 Location: Inside my twisted little mind....
Re: How to reach the measurement of this crease on a fish ba
It comes from trigonometry and geometry. The bisector of the angle at the bottom forms a 22.5deg angle from the edge, the cosine of which is 1/(1+sqrt2). It also happens that the distance from the left corner of the square to the left end of x is the same as the length of the square's edge (y). Since the main diagonal is sqrt2 times the side length, just multiply y by sqrt2 and subtract it from the result.
The equation is x = (sqrt2)y  y.
The equation is x = (sqrt2)y  y.
Re: How to reach the measurement of this crease on a fish ba
I didn't get everything you wrote, but I did get that it's possible to present the problem as the Pythagorean theorem:
y²+y² = (y + x)² right?
Was that what you did?
You mentioned x = √(2)y  y
I can take it one step further x = y(√(2)  1)
If y = 1 then x = 0.41421356237
One more question, is there a shortish fraction close to that number?
y²+y² = (y + x)² right?
Was that what you did?
You mentioned x = √(2)y  y
I can take it one step further x = y(√(2)  1)
If y = 1 then x = 0.41421356237
One more question, is there a shortish fraction close to that number?
Last edited by Gerardo on September 18th, 2018, 1:48 am, edited 1 time in total.

 Senior Member
 Posts: 486
 Joined: April 7th, 2017, 4:54 am
 Location: USA
Re: How to reach the measurement of this crease on a fish ba
http://www.mindspring.com/~alanh/fracs.html
This website might be helpful. I typed in the number and it gave a few fractions:
2/5 = 0.4
5/12 = 0.4167
12/29 = 0.41379
29/70 = 0.41428
70/169 = 0.414201
This website might be helpful. I typed in the number and it gave a few fractions:
2/5 = 0.4
5/12 = 0.4167
12/29 = 0.41379
29/70 = 0.41428
70/169 = 0.414201
My instagram: https://www.instagram.com/theplantpsychologist/
My youtube: https://www.youtube.com/channel/UCJPCcy ... U8oLMv5WpQ
My flickr: https://www.flickr.com/people/185437267@N03/
My youtube: https://www.youtube.com/channel/UCJPCcy ... U8oLMv5WpQ
My flickr: https://www.flickr.com/people/185437267@N03/
Re: How to reach the measurement of this crease on a fish ba
Awesome webpage! Thanks NeverCeaseToCrease .