‽ Born in 220 B.C. and lived until 280 B.C.

‽ Lived in Northern Wei Kingdom during 3rd 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 with3 X 2n sides in terms of the length of the side of a regular polygon with 3 X 2n-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 pn-1 ,

the length of the side of a regular polygon with 3   2n-1 sides, so AY has length pn-1/2. Thus OY has length

√(r2 - (pn-1/2)2).

Then YX has length r - √[r2 - (pn-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 - pn-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.