There are products that are in almost everyone’s life. They are always in front of our eyes, but we hardly think about the math behind them. For example, there is a reason why beverage cans are produced 330 ml instead of 350. Or why carboys are produced as 19 liters instead of 20? We regularly prepare content to answer these questions. Today, we will explain why the A4 paper size used by everyone is produced as 21×29.7 cm instead of 20×30 cm. Maybe you used a lot of A4 paper before, but you didn’t pay much attention to the dimensions, but there is a reason why these papers are produced in fractional sizes.
An A4 paper is 210×297 millimeters. If we give this in inches, we will see a measurement of 8.3×11.7 inches. So why is this paper odd? Did they use this unit of measurement just because it is more beautiful like that? Today we will tell you the math behind the A4 paper.
Why is A4 paper size fractional? There are “A” paper sizes including
A4 paper. These start from A0 and continue up to A8. The math behind these papers, called the ISO A series, is that they all have the same aspect ratio. In other words, when you divide the 29.7×42 cm A3 paper into two from its long area, you will get A4. When you divide 42 by 2, you get 21. This is 21×29.7; ie it gives the size of A4 paper. The entire A format, in which A4 is included, has an aspect ratio of 1:1.414. The mathematical formula of the papers in the A series is 1:√2. In other words, this ratio will be valid in A1 as well as in A4.
Let’s explain why the A4 paper is fractional with examples.
For example, let’s say you divide a square piece of paper into two with the same logic. Let this paper be 40×40 cm. When you divide this page into two, it will be 20×40 cm. Paper that originally had a 1:1 ratio will change to a 1:2 ratio when split. When you divide most of this paper into two, it will reach a 20×20 cm page. In other words, you can reach the aspect ratio that you can reach in A format in one move in two moves on square paper.
Let’s give an example over a rectangle this time to understand the subject better. Moreover, this paper should be 20×30 cm, which is close to A4 format. Our paper is in 1:1.5 format at the first stage. When we divide the long side of this paper, we will see a 15×20 cm paper. At this stage, we see that our paper has an aspect ratio of 1:1.25. The main reason for the standardization of the A format is that unlike other formats, it can always stay in the same aspect ratio. You can use a work done on A4 paper in A3 ratio by keeping the same proportions.
Date and acceptance stage of “A” paper sizes including A4
A series paper sizes were first accepted in Germany in 1922 . This standard, which has been used in Germany for many years, became a standard in 1975 under the name ISO 216. This standard is now used all over the world, except for North America and Canada.
According to this standard, each paper is obtained by dividing the long side of the previous one into two equal parts. The basic dimension is A0; It has a size of 841×1189 mm, which corresponds to 1 square meter. The resulting square meter area is not square, but rectangular. According to the math built on it, the aspect ratio of this rectangle is always preserved in other A formats. This aspect ratio also equates to 1:1.414.
Today we explained to you why the A4 paper format has the dimensions 21×29.7 cm, not 20×30. If you want more content like this, you can reach us in the comments section.
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