Geometry and topology · Maths EE idea · Accessible
Testing golden-ratio claims mathematically
A research question to start from
Which properties of the golden ratio can be proved (in the pentagon, continued fractions and Fibonacci numbers), and how can claims about it in art be tested?
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
Separates genuine mathematics from myth: proofs first, then a careful test of a claim.
Mathematics you would need
- Quadratic equations
- Similar triangles in the regular pentagon
- Continued fractions
- Measurement error
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
- Prove the golden ratio's appearances in the pentagon.
- Show its continued fraction and relate it to Fibonacci ratios.
- Design a fair test of a claimed golden-ratio proportion and evaluate it.
Scope and difficulty
Accessible. Accessible; the testing section gives the evaluation.
Pitfalls
- Repeating myths uncritically.
- Mostly art history.
Where to start reading
Search a library catalogue or a university's open lecture notes for: golden ratio pentagon proof; golden ratio myths measurement. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).