by Yossi Nir
Edited by Jane Rosemarin
Two versions of the Square Root Box, designed and folded by Yossi Nir. See PDF diagrams.

My name is Yossi Nir. I am an electrical engineer by profession, and origami is my hobby in addition to photography, computers, sculpture and baking.

The design and creation of Origami models presents a thought challenge for me that ultimately provides flawless activity and a big smile.

My first book, “Origami - A Love story,” was published by Amazon in 2021. My fifth book, “Selected Collection of Origami,” was published by Amazon on April 28, 2023. This collection has 50 origami models that I created.

My favorite models are geometric. I like to explore this niche in origami. Geometric models are usually 3D, and are both impressive, and surprising.

In most models, it is possible to identify the mathematical/geometric shape. There are also cases where the mathematics is less obvious, and then the creator must give it a name. The Origami Square Root Box is one that I had to give a name to.

The reason for the name is that if you want to calculate the size of the edge of the square base, then you need to determine the square root of a number, as described in the drawings of the model.

Enjoy the folding and the calculations.


August 10, 2023 - 11:17am Alagar_Venkataswamy

I wanted to calculate the size of paper I have to use to get a (gift) box of a size I needed – by using the crease pattern I used for the folds.

We essentially came up with the same formula anyhow!

Referring to the diagram – below - with the creases made:
o size of the paper: p
o diagonal of this square paper: d = sqrt(p^2 + p^2) = sqrt(2)*p
o As could be seen in the image of the creased paper, the diagonal is divided into 8 equal parts
o The blue colored square area, that would be the bottom of the box to be made, takes up 2 of the 8 parts, or ¼, of the diagonal
• Or, sides of the bottom of box, s = (¼)*d = (¼)*sqrt(2)*p
• Height of the box, h = (1/8)*d = (1/8)*sqrt(2)*p
o Size of the paper to use in terms of the needed size of the box:
p = 4*s/sqrt(2) = 2*sqrt(2)*p = 2.828*s

(Could not include picture/drawing.)