History of mathematics · Maths EE idea · Solid
Pi in ancient China
A research question to start from
How did Liu Hui's polygon method and later refinements approximate π, and how efficient were they compared with Archimedes' approach?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A cross-cultural comparison of methods, worked mathematically.
Mathematics you would need
- Areas of polygons
- Recurrences
- Error estimates
- Convergence comparison
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Reconstruct Liu Hui's area method.
- Explain the acceleration idea he used.
- Compare with Archimedes' perimeter method.
Scope and difficulty
Solid. Solid; check historical claims in scholarly sources.
Pitfalls
- Unsupported historical claims.
- Little mathematics.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Liu Hui pi algorithm polygon area; Zu Chongzhi 355/113. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).