The Chinese calculated pi using geometric methods, particularly by approximating the area of polygons inscribed within a circle.
Liu Hui's Method
Liu Hui, a Chinese mathematician in the 3rd century AD, developed an algorithm to approximate π based on calculating the area of N-gons (polygons with N sides) inscribed within a circle. This contrasts with the Greek mathematician Archimedes' method, which focused on the circumference of polygons. Liu Hui's approach is considered one of his most significant contributions to ancient Chinese mathematics.
Details of Liu Hui's Algorithm:
- Area Calculation: Liu Hui started with a hexagon inscribed in a circle. He then progressively doubled the number of sides of the polygon (12-gon, 24-gon, 48-gon, and so on).
- Iteration: By continuously increasing the number of sides, the polygon's area gets closer and closer to the circle's area.
- Approximation of Pi: Since the area of a circle is πr², where r is the radius, and knowing the radius, Liu Hui could approximate π by calculating the area of these increasingly complex polygons.
- Result: He calculated π to be approximately 3.1416, a significant improvement over previous estimates.
- Advantage: The main advancement in Liu Hui's method was that it was based on the calculation of N-gon area, instead of the circumference.
Other Contributions
While Liu Hui's work is most prominently known, other Chinese mathematicians also contributed to approximations of pi over time, often building on or refining existing methods.
In Summary, the Chinese calculated pi through methods such as:
- Inscribing polygons within a circle.
- Calculating the area of the polygons.
- Increasing the number of sides of the polygon to get a more accurate approximation of the circle's area.
