### How to reach the measurement of this crease on a fish base?

Posted:

**September 17th, 2018, 10:11 pm**
by **Gerardo**

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

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### Re: How to reach the measurement of this crease on a fish ba

Posted:

**September 17th, 2018, 10:36 pm**
by **Baltorigamist**

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.

### Re: How to reach the measurement of this crease on a fish ba

Posted:

**September 18th, 2018, 1:07 am**
by **Gerardo**

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?

### Re: How to reach the measurement of this crease on a fish ba

Posted:

**September 18th, 2018, 1:26 am**
by **NeverCeaseToCrease**

http://www.mindspring.com/~alanh/fracs.htmlThis 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

### Re: How to reach the measurement of this crease on a fish ba

Posted:

**September 18th, 2018, 1:50 am**
by **Gerardo**

Awesome webpage! Thanks NeverCeaseToCrease

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