This is something that always annoys me when putting one A4 letter in a oblong envelope: one needs to estimate wherein to placed the creases when folding the letter. I normally start native the bottom and also on eye estimate whereby to fold. Climate I turn the letter over and also fold bottom come top. Many of the time finishing up v three various areas. There have to be a way to perform this exactly, without using any tools (ruler, etc.).

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Fold double to achieve quarter markings in ~ the record bottom.Fold along the line v the height corner and the 3rd of these marks.The upright lines with the very first two marks intersect this inclined line at thirds, which enables the final foldings.

(Photo through Ross Millikan listed below - if the image assisted you, you deserve to up-vote his too...)

Here is a photo to go with Hagen von Eitzen"s answer. The horizontal lines space the result of the first two folds. The diagonal heat is the 3rd fold. The hefty lines are the points at thirds for folding into the envelope.

\$egingroup\$ "over 's signature" doesn't mean "overwriting 's signature" \$endgroup\$
This is both helpful (no extra creases) and specific (no guessing or estimating).

Roll the document into a 3-ply tube, v the end aligned:

Pinch the paper (crease the edge) where I"ve attracted the red line

Unroll

Use the pinch mark to show where the folds must be

This equipment works just with a sheet of file having aspect ratio the sqrt(2) (as A4 has).Only two extra folds required.

Roll in to a cylinder till both edges space opposite to each other.Fold the points wherein the edges touches the paper. (Squish the cylinder native left and also right)

Approximation method:

Assume a 120 level angle and fold as presented below.For accuracy, match edge-side to any type of of the various other two sides.

Beyond the more geometric methods explained so far, over there is an iterative algorithm (in practice, as an exact as any exact method) as result of Shuzo Fujimoto that i think nobody mentioned. In fact, the following an approach can be generalized to any type of shape, size and number of foldings.

Let me denote \$d_l\$ the street from the left side of the paper to the very first mark ~ above the left and \$d_r\$, the street from the best side to the ideal mark. Come simplify, assume the the lenght of the next you want to division is 1.

Make a very first approximation because that \$d_l\$. You want \$1/3\$, however imagine you take \$1/3+varepsilon\$ (\$varepsilon\$ being part error come the right or come the left). Thus, top top the right you now have actually \$2/3-varepsilon\$.

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Next, divide the right component into 2 for the very first approximation that \$d_r\$ (by taking the ideal side that the record to your first pinch; again, simply a pinch). This provides you \$d_r=1/3-varepsilon/2\$, thus, a far better approximation!

Now, repeat this procedure ~ above the left. ~ above the left part you now have \$2/3+varepsilon/2\$. Take the left side of the file to the 2nd pinch to acquire a 2nd approximation the \$d_l = 1/3+varepsilon/4\$. Note that, after 2 pinches, you have diminished your initial error to a quarter!

If her initial guess was precise enough, you will certainly not require to continue more. But, if you need an ext precission, you just need to repeat the procedure a pair of time more. For instance, one initial error the \$varepsilon=1\$cm reduces to much less than 1mm (0.0625mm) after ~ repeating the iteration twice.