### Introduction

A great mathematician called Liu Hui emerged from Cao Wei, which was one of the Three Kingdom divisions in Chinese History. His mathematical findings and interests are still valued by the world. He descended from the Marquis of Zixiang (Han Dynasty). Some people also believed that he attempted to measure the sun’s shadow.

### Early Life

Liu Hui was born in Zibo, Shandong, about 220 (fl. 3rd century).

### Mathematical activities

Lui Hui along with editing also published a book in 263 AD which contained the solutions to mathematical problems in the well-known Chinese book titled “The Nine Chapters on the Mathematical Art”. He is classified as one of the most famous mathematicians of ancient China, and falls in the line along with Zu Chongzhi.

His mathematical answers were in the form of decimals fractions.

Liu also commented on a proof which seemed identical to the Pythagorean Theorem. He suggested that the theorem’s figure drawn diagram gives “the relations between the hypotenuse and the sum and difference of the other two sides whereby one can find the unknown from the known”, this sentence was actually inclusive within what he ‘called’ the diagram.

When it came to plane areas and solid figures, he was a pioneering contributor to ‘empirical’ solid geometry. For instance, he can be accredited for finding out that a wedge with a rectangular base and both sloping sides could be broken into a pyramid and also a tetrahedral wedge.

Liu Hui also discovered that a wedge that has a trapezoid base and both sloping sides could be transformed into two tetrahedral wedges segregated by a pyramid.

In Nine Chapters he proposed an algorithm for the calculation of pi (π), he also started the Cavalieri’s principle which was to determine the volume of a cylinder; however this work was later finished by Zu Gengzhi. His work comprised of commentaries, even though there were a few errors, he is still regarded as a well-reputed mathematician in the historical context.

He also compiled a separate appendix in 263 AD which was known as “The Sea Island and Mathematical Manual”; it covered many problems related to surveying. It consisted of pragmatic geometry problems along with the measurement of the heights of Chinese pagoda towers.

Liu Hui through his commentary on “Nine Chapter” was able to contribute thought analysis on building canal and river dykes, which amounted up to the labour and material requirement, alongside with the time needed for construction. His work proved to be helpful to the progress of cartography and it was acknowledged as advancement within that period too.

In conclusion, he was a mathematician who dabbled in the field of cartography and mathematics simultaneously, and managed to bring about mathematical revelations and ideas in that ancient historical time.