Eye week: A4 paper to Lichtenberg ratio

Dabao:

A4 paper you are not strangers to, right? Look at your textbooks, and the English materials I printed for you the other day, but they are all A4 specifications.

A4 paper is the most commonly used paper specification in life. It is widely used in life, probably related to its size.

In fact, all A Series paper aspect ratios are the same. In the A (A0, A1, A2, A3, A4, A5) series of paper, after the paper pair of the previous serial number is cut, two pieces of paper of the size of the back serial number can be obtained, such as A0 pair can get 2 sheets of A1, and so on, A3 pair of cut can get two pieces of A4 paper.

As long as you have a certain A series of paper at hand, you can make any size of A series. This feature of the A specification series makes it easy to convert between them and easy to use.

This convenience is brought about by the special aspect ratio of A-series paper, the Lichtenberg ratio of 1.414:1.

Where is Lichtenberg sacred?

Lichtenberg (1741-1799) was a German Enlightenment scholar of the second half of the 18th century, a prominent thinker, satirist, political commentator, and physicist.

In 1786, Lichtenberg wrote a letter to the scientist Johann Wolfgang von Neumann. Beckman, introducing him to a problem he had given his students. He asked students to calculate a paper size and asked the paper to fold in half so that the length-to-width ratio would remain the same. He enclosed the letter a piece of paper that met the requirements, which he considered "pleasant and very special," and said in the letter that the size had already been adopted by papermakers.

In fact, Lichtenberg gives students out the puzzle of Dorothea. Schlozer had encountered and solved it as early as 1755. Schlozer (recognized as the first woman in German history to earn a doctorate in philosophy) is one of five elite female teachers at German universities. She took this answer to the old marshal in 1755 and did not get a response.

The 1.414:1 size law dates back more than a thousand years, when the Municipal Archaeological Museum of Bologna (Italian city) displays a limestone plate describing what is estimated to be the earliest standard paper size. The plate is an ancient artifact from 1389, and the inscription on it lists four sets of rectangular sizes, two of which conform to the 1.414:1 rule.

The A4 paper that conforms to the Lichtenberg ratio also contains a silver ratio - 2.414. As long as the short side of the A4 paper is used as the side length, a square is drawn and cut out, and the remaining rectangle's aspect ratio is the silver ratio. The aspect ratio of A4 paper is 1.414:1, and the aspect ratio of the remaining rectangles using the above method will be 1:[1.414:1] = 2.414.

The silver ratio of 2.414 is related to the Pell sequence, while the golden ratio of 1.618 is related to the Fibonacci sequence.

The Lichtenberg ratio makes the use of paper more convenient, and the golden ratio and the silver ratio are widely used - the golden ratio line for photographs, the silver proportion mosaic on the wall...

Math is amazing.

Philosophers are great.