Liu Hui was amazing! There were so many people in Ancient China that history looked over for a while. I'm glad I'm
from the 23rd century where we have such an understanding of how math was viewed from different cultures. Liu Hui had a method
of approximating pi that was similar to Archimedes' way, even though they had no communication with each other over such
long distances. They both used the method of calculating the perimeter of a polygon inscribed in the circle, as well as the polygon
circumscribed around the circle. That would then give them a lower and upper bound, since the circumference of the circle would be greater than
the inscribed polygon, but less than the circumscribed polygon. Experiment with this applet to see how Liu Hui and Archimedes calculated this.
Both Liu Hui and Archimedes used this method, but Archimedes only went to a 96-gon and got 3.140845070422535< pi <3.142857142857143
or 223/71< pi <22/7. Liu Hui took the same idea, but went to a 192-gon to find that pi is close to 3.141864 and is credited
with finding a more accurate approximation of 3927/1250 or 3.1416. Once he got this answer, he decided to check his work.
That's an important thing to do while doing math problems. He went a little extreme and used a 3072-gon to check.
He also edited the famous book called The Nine Chapters on the Mathematical Art. That's where his approximations of pi were
found.
Also in The Nine Chapters was his method for solving a system of linear equations. It's similar to the method used in the West called
Gaussian elimination. This video shows the
method that Liu Hui used to solve a system of equations. We better scoot along to our last stop. I think you'll really like this mathematician.
Let's go visit our friend ...