‽ Born in 220 B.C. and lived until 280 B.C. ‽ Lived in Northern Wei Kingdom during 3 rd Century Nobody really knows anything else about his life!

He found a recurrence relation to express the length of the side of a regular polygon with 3 X 2 n sides in terms of the length of the side of a regular polygon with 3 X 2 n-1 sides. This is achieved with an application of Pythagoras's theorem.

In the diagram we have a circle of radius r with center O. We know AB, it is p n-1, the length of the side of a regular polygon with 3 2 n-1 sides, so AY has length p n-1 /2. Thus OY has length √(r 2 - (p n-1 /2) 2 ). Then YX has length r - √[r 2 - (p n-1 /2) 2 ]. But now we know AY and YX so we can compute AX using the Gougu theorem (Pythagoras) to be √{r[2r - √(4r - p n-1 2 )]}.

+ The Nine Chapters of Mathematical Art is a book of two hundred forty-six problems dealing with mathematics. + It was the best math book that the Chinese had in the third Century. + Liu Hui wrote two commentaries in this book about proving algorithms concerning the area of a circle and algebraic operations

Proved algorithms for arithmetic and algebraic operations o adding fractions o solving systems of equations

Liu Hui noted a gap in the Nine Chapters that didn’t allow one to do problems involving celestial distances. He surveyed algorithms that amounted to a kind of Trigonometry to do just this. This work later turned out to be a book called The Sea island Mathematics manual.