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Liu Hui's Method (China, 263 CE)
Liu Hui's Method (China, 263 CE)
Liu Hui refined the calculation of π using many-sided polygons:
Starting with a 6-sided polygon
Then 12 sides
Then 24 sides
Doubling to 48, 96, 192, 384...
Liu Hui used the principle of repeatedly doubling
the number of sides to achieve greater precision.
With a 3072-sided polygon, he calculated:
π ≈ 3.14159
The Magic Circle Number!
1
Diameter = 1
Circumference = 3.14
3.14 ÷ 1 = 3.14
2
Diameter = 2
Circumference = 6.28
6.28 ÷ 2 = 3.14
3
Diameter = 3
Circumference = 9.42
9.42 ÷ 3 = 3.14
4
Diameter = 4
Circumference = 12.56
12.56 ÷ 4 = 3.14
No matter what size cookie:
Circumference ÷ Diameter = 3.14159... = π
This special number π (Pi) never changes!