Flashlights & Torches

Do you really understand A4 paper?

Learn Mathematics, on the star coordinates. Hello, here is a star coordinate headline.

A4 paper, can be said to be a piece of paper in our lives, very practical, not only, there are some stars and netizens on the Internet, with the size of A4 paper, to show their own small Variety, the beautiful name “A4 Waist”. There is no “A4 waist”, it seems that it has become an important criterion that judges a bad body, but do you really understand the A4 paper? Have you ever thought about why A4 paper called A4 paper? Also, the standard size of A4 paper is 297 mm long, 210 mm wide, this size is not good at all, it is also troublesome, why not be 300 mm, 200 mm wide? Today, I will come to uncover the mystery of A4 paper.

Speaking of the standard of paper size, in the 1920s, the Germans have been developed and incorporated into their industrial standard system, and later promoted, the international standardization organization (ISO216) is defined, mainly Divided into three major categories, respectively

Paper, B paper, and C above.

Among them, the i is the most extensive application. Next, let’s take a look at the sacred.

A number of paper is actually a number of different sizes of paper. For the convenience of distinguishing, we add a number behind A, starting from the area of ​​1 square meter, then A1 paper, A2 paper, A3 paper, A4 paper …

Among them, the A1 paper is gotten by the A0 paper along the long side, then the A4 paper we mentioned at the beginning is naturally the A0 paper in the long side of 4 times.

Here you suggest that you open the document, look at the pictures in the document, it will be more likely to understand.

Now we know the origin of the A4 paper name, how is its size specified? Depending on the image in the document, you can get the size of the A0 paper to the A8 paper. We respect the long and wide ratios of these eight paper, I put the calculated results in the form of a form, if you are interested You can open a manuscript.


I think you must find it, the length of these eight paper is almost the same, if you are sensitive to unreasonable numbers, you will be surprised to find that this ratio is close to the root number 2, why?


First we know,

After a rectangle is folded along the long side, the new rectangle has a length equal to the width of the original rectangle, the width of the new rectangle is equal to half the length of the original rectangle.

Now we assume that the length of the rectangle from the re-folded N times in the long side of the A0 paper.




If n + 1 time is changed to the rectangle after folding


So because the length and wide ratio always remain unchanged, then

From this we can get:

That is, the ratio of the length and width of the A0 paper is the root number 2.

It turns out that a rectangle has a rectangle that is equal to the long side, the length and width ratio is equal, then this ratio can only be the root number 2.

A further because the area of ​​A0 paper is 1 square meter, the ratio of the binding long and wide is the root number 2. We can calculate the size of the A0 paper, then A1 paper, A2 paper, A3 paper, A4 paper, etc., these paper The size can also be calculated, I put the size of the No. A paper in the form of a form, if you are interested, you can take a look at the manuscript. Now you understand why A4 paper size is 297 mm long, 210 mm wide!

Finally, I want to ask you to think about a question: Why should we specify that each size of the paper, long and wide ratio is the same? Where is the benefit of this? Welcome to the commentary to make an interaction, share your opinion.

The above is today’s headline content, I hope he will be inspired by you, let’s see you tomorrow.

Reference: [1] Li Ya. A4 paper size – Application of optimal score [J]. China Training, 2017, (07): 221.


[2] Jin Yiming. Magical Mathematics (1) [M]. Hangzhou: Zhejiang Business University Press, 2018.

Centus: Xiao Qian

Tell: Xiao Qian