Fold paper

Types of folds:

1. Wrap fold
2. Window folding (altar folding)
3. eight-sided window folding
4. Leporello or zigzag folding
5. Parallel center fold
6. Cross fold

Paper folding is the folding of sheets of paper .

For mechanical folding see also: Folding (paper technology)

Merging of documents

A letter unfolded paper

Letter paper in DIN A4 format is folded twice horizontally in business correspondence and sent in a DL envelope. If an envelope with an address window (bottom left) is used, according to DIN 5008 there are two variants ( A and B ) for the height of the letterhead and the adjoining position of the address field and two lower fold marks . The upper edge is 87 or 105 mm from the upper edge of the paper, the lower one 105 mm lower. First the lower (approximate) third of the letter can be folded forwards and upwards and then the double layer opposite the upper third can be folded backwards, which creates a zigzag fold and the letterhead remains visible.

If the positions are on the fold marks, the folded letter is still 105 mm high (like a postcard) in order to fill the envelope sufficiently, to be able to move only a little, and so the address field is legible within the envelope window. It is also guaranteed that no fold runs through the area of ​​the folder perforation (d = 6 mm at 80 mm center distance), which keeps its dimensions stable.

This "Z" -fold - viewed from the left - lies well again on the table and holds multiple pages together well.

The alternative spiral fold - a "C" when viewed from the right - can indeed wrap something like a banknote more securely, but it blocks something when several sheets are folded together and is therefore less flat.

After a cross fold in the middle, an A4 letter fits into a C5 envelope, with a cross fold into a smaller C6 envelope. Before letters were sorted by machine at high speed, these folds - only the middle of the three open edges glued to the flap of an address label - could still be sent without envelopes and thus extremely inexpensive until around 1990 - relevant for small mass mailings from associations, for example.

Up to three sheets (A4) of normal thick paper (around 80 g / m ² ) can be cross-folded together, and correspondingly more of the much thinner airmail paper. Thin paper needs a firm table surface to fold. Plain paper can be folded particularly well freehand, i.e. in the air and between the tips of the thumb and index or middle finger, by first removing the longitudinal fold (the typeface turning inwards) and then halving it to produce the shorter transverse fold. The continuous longitudinal fold in the reopened state then stiffens a letter better if it is held freely sideways with one hand.

In order to keep an unfolded sheet stable, the middle three fingers typically form a conical hollow under the lower left corner of the sheet, regardless of whether it is oriented in portrait or landscape format, and the thumb presses a wave into the surface that widens , runs diagonally to the top right and efficiently stiffens the sheet. One tries to avoid local creases, i.e. no traces of folds, as when turning the pages of a book. The flexibility and ease of folding of paper is greater along the grain , usually along the sheet.

In many schools in the United States, similar sized paper is folded lengthwise once when it is dispensed. This bundles several sheets of paper from a student and, if the written side is turned inside, creates a certain confidentiality and security against copying.

Drawings, printed works

Folding machine for maps

Correct folding of technical drawings is regulated in DIN 824 . This means that even large papers can be folded out and stored in folders without the perforations running through the characters.

Bookbinding has developed from the formation of longer written works and compilations, also by folding .

To this day, daily newspapers are mostly not bound, but also only delivered folded (see newspaper format ). A folded part can also lie in a stapled part (Sunday Kronenzeitung in a brightly colored glossy journal) or vice versa ( Kleine Zeitung , Sundays). Large format newspapers typically have a cross fold and are divided into several books from a certain number of pages, also in order to improve the fold.

The leporello and cross folds of large maps and the small Z-card best stiffen them if they are not completely unfolded.

Games, crafts and art

Origami product

Folding can be found in many ways as a leisure activity, such as folding paper flowers or paper snakes. One type of particularly artistic paper folding is origami , which comes from Japan . The paper art medium is, for example, the PaperArt biennial in Düren, North Rhine-Westphalia. Napkin folding is also related to paper folding .

Probably the best-known application of paper folding is the paper plane , as it is found among children around the world, forms countless variants, but has also brought it to a world championship.

Folding paper, scissors and possibly glue - frowned upon in origami and aviator construction - result in hobbies such as the paper craft sheets , in which cut and folded parts are modeled into buildings or vehicles. The building of paper bridges has also become a scientific study area of structural engineering . A toy that has become rare today was the paper dress-up doll .

The folding games include heaven and hell .

Mathematical aspects and mind games

A4 sheet of paper folded in 256 layers (eight times), approx. 2.5 cm high

Seven folds of A4 sheets in comparison. The 7th fold no longer keeps its shape

One common thesis is that it is impossible to fold a piece of paper of any size in half more than seven times. This statement is not correct in this general form, because the maximum number of folds generally depends on the thickness and length of the paper used and the required folding force, as well as on whether one always folds parallel or over edge. This is explained by the fact that the thickness of the folded paper increases exponentially , and so does the force that is necessary for a further fold. In addition, the folding edges use more and more paper with increasing thickness, which is why the paper used must have a minimum length.

Example: If a sheet of paper is folded seven times, it then already consists of 2 ⁷ = 128 layers. Commercially available printing paper with a thickness of d = 0.1 mm would then already be 12.8 mm thick. The minimum length of the paper after the n -th fold is now calculated according to the formula (for folding in one direction)

${\displaystyle L(n)={\tfrac {\pi }{6}}\cdot d\cdot \left(2^{n}+4\right)\cdot \left(2^{n}-1\right)}$

to L (7) = 877.8 mm. A sheet of paper in DIN A0 format was therefore required for this .

The estimation was made in 2002 by the high school student Britney Gallian (* 1985), who also demonstrated a twelve fold folding with a special toilet paper.

Numerous mind games and puzzles are also based on folding problems.

Individual evidence

1. ↑ DIN 5008 : 2020-03 Writing and design rules for text and information processing , Section 19 Structure and design of letter forms and templates , Subsection 19.3 Forms
2. ↑ Heaven and Hell. In: mathematische-basteleien.de
3. ↑ Heaven and Hell - traditional. In: origami-kunst.de
4. ↑ How often can you fold paper? In: Broadcast with the Mouse on June 22, 2008, with Ralph Caspers
5. ^ Folding. In: Wolfram MathWorld. Retrieved May 22, 2015 . 
6. ↑ Christoph Drösser ( Right? ): Magical Sieben. In: The time . No. 36, August 26, 2004
7. ^ Clifford Pickover, Math Book, Sterling Publ., 2012, p. 504