The Origami Forum

Hello everyone,

I am working on a model which requires height/width ratio of 3:5. I don't have origami paper to work with, so what I usually do is get a square from A4 paper which is actually very easy to do, just fold a diagonal and get rid of the other part. However when it comes to this specific ratio, it gets a bit more complicated.

The ratio of A4 format is 1 by square root of 2 with precision of 4 decimal points, so 1:1.4142 (height by width that is, if we consider that the longer side is width). We can measure height very precisely, it is 21 cm. We can then calculate the width, 21 * 1.4142 = 29.6982, so let's just say 29.7 cm.

At first I used to find two whole numbers (because I found them easier to work with) which satisfy these requirements: their ratio is 3/5 and they are smaller than 21 and 29.7 (so they fit in paper). These are 15 and 25. So the height would be 15 cm and width 25 cm.

While the calculations are correct, the measurement and cropping usually doesn't go as smooth. The lines are almost never parallel and/or straight. With time I figured that using whole numbers maybe isn't as good, because then I have to crop both width and height, which leaves more room for error. It is not that much of a problem if I have milimeter paper lying around but that is a rare case.

What I did next was, tried to find a way with which I can utilize one entire side of a paper, while cropping only one side, which would reduce cropping error pretty good. Using a bit of maths:

1) Say we use the whole height

21 / x = 3 : 5
3x = 105
x = 35

So the width would have to be 35 cm but that is not possible because max is 29.7 cm

2) Say we use the whole width

x / 29.6982 = 3 / 5
5x = 89.0946
x = 17.81892

So the height would be about 17.8 cm, pretty good. Now I only need to crop height which is more precise. But there is still room for error in the measurement itself, and in parallelness of two height sides.

LONG STORY SHORT

Is there a better way to do this then measuring 17.8 cm on both height sides, drawing a line between those two points and cutting/ripping on that line?

Thank you for your time!

It seems like the best way. Or just measure one side and use the paper's edge to give you the 90 degree angle you need. I don't see why it would create such a big error, a millimeter is usually small enough a mistake to not even notice. Maybe just measure and fold/cut a bit more slowly?

If you want to be all mathematical about it you could use Lang's reference finder. It's definitely not practical though, but you wouldn't need to measure anything with a ruler.

Yeah I see, so I just kinda pinch 90 degrees on one side when measured and use it as reference, then just align the paper right at the other side. That's way better, thanks!

The problem was not so much in the absolute precision, but more in the fact that I couldn't measure both sides with same precision. Because of that, when I cut through the line, the sides wouldn't be really parallel, which gets annoying when folding. This fixes it, indeed, and can be applied to pretty much any size.