Zu Chongzhi, a famous mathematician in the Southern and Northern Dynasties in China, once got two important achievements related to pi.

First, he calculated the pi between 3. 14 15926 and 3. 14 15927. Second, he used two 22/

7 and 355/ 1 13 approximately represent pi. In connection with this, there are already representations of these values, but

There are also some improper words. Give a few examples:

Hu Zuoxuan's book Unsolved Problems in Mathematics 12 pages;

The π value calculated by him (Zu Chongzhi) is between sparse and dense, that is, 22/7 < π < 355/ 1 13.

It can be seen that Mr. Hu Zuoxuan called 22/7 the sparsity rate.

Ren Xianmiao interesting math 365 days 144 pages:

The sparsity of π is 22/7 and the density is 355/ 1 13. The secret rate is also called the ancestral rate.

The Art of Mathematical Discovery written by Yang Shiming and Wang Xueqin is also called 22/7 sparse on 144 page.

However, the name sparse is wrong. This wrong context: Liang Zongju's historical allusions to mathematics.

This 240-page book is clearly discussed and quoted as follows:

22/7 clearly wrote "approximate rate", but quite a few articles were mistakenly written as "sparse rate" and may be published.

Accidental typographical error (or clerical error). For example, Kebiao Zhang's The Story of Arithmetic (Ming Kai Bookstore, 1935).

P 140 is correctly written as approximate rate, but wrongly written as sparse rate on P20 1. 1951February 10 People's Daily 3

Edition published China's "Mathematics is a discipline that Chinese people are good at" ... The article mentioned that "(Zu Chongzhi) used 22

/7 and 355/ 1 13 are thinning rate and density rate "... Later, a large number of books and periodicals used the name" thinning rate ". in fact

Hua has corrected this name in his book On Zu Chongzhi's Pi (June 1962).

Come here, and put Sui Shu's original text in front of the book, and add emphasis under the secret rate and contract rate to cause

Attention. However, until recently, people's silence rate had an incorrect name.

This passage by Liang Zongju has clearly explained the problem of porosity.

But there are still some questions about the ancestral rate.

On pages 24 1 and 242 of the same book, Mr. Liang Zongju discussed the issue of ancestral rate and pointed out that "ancestral rate" should be

This refers to Zu Chongzhi's secret rate.

Xie Enze and Xu Benshun's Thinking Methods of Mathematicians in the World. Page 157:

Therefore, in 19 12, Japanese mathematician Kazuo Mishi proposed that π = 355/ 1 13 should be called "ancestral rate".

But Shen "Introduction to Arithmetic" on page 387 thinks

Zu Chongzhi's contribution to arithmetic is very great. At the end of Liu Song Dynasty, the calculation of pi was recorded in his Composition.

Things, to say that this rate is in the History of Arithmetic Development between China and Japan.

3. 14 15926