History of mathematics · Maths EE idea · Solid
Tangents before calculus
A research question to start from
How did Fermat and Descartes find tangents and maxima before calculus, and how do their methods relate to the derivative?
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
Historical methods worked through and compared with the modern limit definition.
Mathematics you would need
- Adequality
- Descartes' method of normals
- Limits and derivatives
- Polynomial algebra
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
- Work through examples with each historical method.
- Explain each in modern terms.
- Evaluate their logical gaps and how limits fixed them.
Scope and difficulty
Solid. Solid.
Pitfalls
- Narrative only.
- No modern comparison.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Fermat adequality tangent method; Descartes method of normals. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).