**Liu Hui** was a Chinese mathematician who wrote a commentary of the *Nine Chapters on the Mathematical Art*.

- This situation lasted for about sixty years, from 220 to 280, which must have been almost exactly the period of Liu Hui's life.
- What influence the events of the period had on Liu Hui is unknown, for nothing is known of his life except that he wrote two works.
- That no record of Liu Hui's life was written, or at least if it was it was not considered worth preserving, does not mean that he was particularly obscure during his lifetime.
- The only precise information about Liu Hui comes from a later work which states that he wrote his commentary on the Nine Chapters on the Mathematical Art in the fourth year of the era of the Jingyuan reign of Prince Chenliu of the Wei, which gives a date of 263 AD.
- What exactly was is the text that Liu Hui is commenting on?
- Liu Hui himself believed that the text which he was commentating on was originally written around 1000 BC but incorporating much material of later eras.
- Let us give some dates for the events Liu Hui describes.
- He ordered all books to be burnt in 213 BC and Zhang Cang, whom Liu Hui refers to, did his reconstruction around 170 BC.
- Most historians, however, would not believe that the original text of the Nine Chapters was nearly as old as Liu Hui believed.
- What Liu Hui added was a more mathematical approach in providing at least principles on which the calculations are based.
- Liu Hui also shows that he understands that some of the methods of the original text are approximations, and he investigates the accuracy of the approximations.
- This is achieved with an application of Pythagoras's theorem, which Liu Hui knew as the Gougu theorem.
- We must emphasise that, of course, Liu Hui did not use algebraic notation as we have done above, nor did he use the number system that we have used.
- Other interesting examples of Liu Hui's contributions to the Nine Chapters on the Mathematical Art is in Chapter 5 on engineering works, where he computes the volume of various solids such as a prism, pyramid, tetrahedron, wedge, cylinder, cone and frustum of a cone.
- The other work which we mentioned above by Liu Hui is Haidao suanjing or Sea Island Mathematical Manual.
- Since we have no information about Liu Hui's life, can we at least deduce some information about him from his work?
- Liu Hui was a learned man, not only having great expertise in mathematics but also being familiar with the literary and historical classics of China.

Born about 220, Wei, China. Died about 280, China.

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Ancient Chinese, Chinese, Origin China, Puzzles And Problems, Special Numbers And Numerals

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive