As one of the four ancient civilizations in the world, China has made many outstanding achievements in the history of mathematics development. For example, the discovery and proof of Pythagorean theorem, the invention and use of "0" and negative numbers, decimal notation, Zu Chongzhi's calculation of pi, and quaternization of equations are all contributions to the field of ancient mathematics in China and occupy an important position in the history of world mathematics.

The brilliant achievement of China's ancient mathematics is to discover and prove that Pythagorean theorem is a basic geometric theorem in the process of human understanding mathematics, one of the important mathematical theorems discovered and proved by human beings in the early days, one of the important tools to solve geometric problems with algebraic ideas, and one of the ties of combining numbers with shapes. Pythagorean theorem is a special case of cosine theorem.

Several ancient civilizations in the world, such as ancient Babylon and ancient Egypt, have studied this theorem successively. China is one of the countries that have known Pythagorean Theorem for a long time, which is called "Quotient Theorem". The ancient astronomical work Zhou Parallel Calculations, written in 1 century BC, recorded what the minister Zhou Gong said when he asked the royal mathematician Shang Gao, including Pythagorean theorem.

The content of this passage is that Duke Zhou asked, "I heard that you are very proficient in mathematics. Excuse me: there is no ladder to go up in the sky and no ruler to measure on the ground. How do you get some measurement data about the height of the sky and the ground? "

Shang Gao said: "Numbers come from the understanding of figures of circles and squares." There is a principle: when the moment of a right triangle gets a right-angled side' hook' equal to 3 and the other right-angled side' chord' equal to 4, then its hypotenuse' chord' must be 5. "

This dialogue is an early record of "Gousan, Gusi and Wuxian" in China's ancient books.

In modern mathematical language, the sum of squares of the lengths of two right-angled sides is equal to the square of the length of the hypotenuse of any right-angled triangle. It can also be understood that the difference between the squares of two long sides is equal to the square of the short side.

Based on the above sources, Chinese scholars generally call this theorem "Pythagorean theorem" or "quotient theorem".

Shang Gao did not answer the specific content of Pythagorean Theorem, but Chen Zi, the descendant of Duke Zhou, used his knowledge of the sun and the earth to measure the shadow of the sun through Pythagorean Theorem, thus determining the height of the sun. This is the scientific practice of ancient China people using Pythagorean theorem.

Chen Zi, the descendant of Duke Zhou, also became a mathematician. He described in detail the whole scheme of measuring the height of the sun. Chen Zi was an authority on mathematics. Except for Regret for the Past mentioned in the last section, the rest of Zhou Yun's book is all about Chen Zi.