History of mathematics · Maths EE idea · Accessible
The rabbits and beyond: Fibonacci's problems
A research question to start from
How can the rabbit problem and other problems attributed to Fibonacci be solved, and what identities about Fibonacci numbers can be proved from them?
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 problems as a route into recurrence relations and identities you prove.
Mathematics you would need
- Recurrence relations
- Proof by induction
- Fibonacci identities
- Closed forms
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
- Solve the rabbit problem and state its assumptions.
- Prove several identities by induction and by counting.
- Derive a closed form.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- Nature myths.
- Identities without proof.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Fibonacci identities proofs induction combinatorial; Liber Abaci problems. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).