The Mathematical Theories of Liu Hui


Since in previous posts, I have already introduced some information about Liu Hui and the contributions he had in the history of ancient mathematics. In this post, I would like to give you more introduction regarding his famous work and mathematical theories.  

The Nine Chapters
on the Mathematical Arts
One of the important works of Liu Hui is his detailed commentary on the book The Nine Chapters on the Mathematical Arts.  Compare to the ancient Greek mathematics who were more focused on geometry at that time, the Chinese mathematics were more concentrated on calculation. And this book Nine Chapters contains numerous calculating formulas. In his commentary, Liu did help to give detailed explanations to the correct formulas. For the ones with errors, he demonstrated the possible cause of the errors and provided suggestions for correction accordingly.  

Also another great invention from Liu is his π algorithm. This was considered as his most important contributions as well. He developed this theory with a N-gon area which is different from the other theory developed based on polygon circumference. Thanks to this new way of calculation. Eventually, this new method was applied by Zu Chongzhi who managed to obtained the most accurate eight-digital result afterwards.

Moreover, he had provided some support in proving the Pythagorean theorem as well. He developed a new way to calculate the unknown side in a diagram with the information of the relations between the hypotenuse and the sum and difference of the other known sides. Originally created by ancient Greek mathematician, Liu Hui has helped to further develop and make it prevalent in the Chinese mathematical world.

Clearly, the contribution of Liu Hui to the ancient mathematical world is enormous. The work he accomplished had huge impact in the development of ancient Chinese mathematic. And even some of the inventions still have not yet been over taken. And most importantly, those works even helped the mathematicians to develop their own theories by applying the theories from Liu Hui.

References:

1. Rongzhao M. (1996) Liu Hui’s Theories of Mathematics. In: Dainian F., Cohen R.S. (eds) Chinese Studies in the History and Philosophy of Science and Technology. Boston Studies in the Philosophy of Science, vol 179. Springer, Dordrecht, pp. 243-244
2.   Liu Hui Retrieved March 13, 2018 from https://en.wikipedia.org/wiki/Liu_Hui
3.  Liu Hui’s π algorithm Retrieved March 13, 2018 from https://en.wikipedia.org/wiki/Liu_Hui%27s_π_algorithm


Comments

  1. Jane KeiserApril 5, 2018 at 3:01 PM

    "Since in previous posts, I have already introduced some information about Liu Hui and the contributions he had in the history of ancient mathematics." This is not a sentence...
    "Thanks to this new way of calculation. " This is also not a sentence. It should have a comma at end and connect it to the next sentence.

    Many people don't think that Pythagoras was the first to prove it. So your sentence, "Originally created by ancient Greek mathematician, Liu Hui has helped..." might not really be correct.

    ReplyDelete

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