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1. Liu Hui By: Erica C.

2. Life of Liu Hui • 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!

3. Approximation of Pi He found a recurrence relation to express the length of the side of a regular polygon with 3 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.

4. Approximation of Pi Cont. 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-12)]}.

5. The Nine Chapters • 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

6. Algorithms for Algebraic Operations • Proved algorithms for arithmetic and algebraic operations • adding fractions • solving systems of equations

7. A Gap in The Nine Chapters 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.

8. THE END