Pure maths · Accessible · Dissertation or artefact

Is the golden ratio really everywhere?: a maths EPQ idea

Why it works as an EPQ

You can derive the golden ratio properly and then test popular claims with your own measurements, so the conclusion rests on evidence.

Scope and difficulty

Accessible. Accessible. Keep the testing to one or two claims with careful measurement and error bounds.

The maths

Builds on these A Level topics: Sequences and series · Algebra and functions · Sampling and data.

You would learn:

• Limits of ratios of Fibonacci numbers
• Measurement error and tolerance
• Continued fractions (optional)

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive φ from x² = x + 1 and show the ratio of consecutive Fibonacci numbers tends to it.
2. Collect claims (spirals, faces, buildings, paintings) and decide how each could be tested.
3. Measure a sample, say what tolerance counts as 'golden', and justify it.
4. Conclude which claims survive and why so many do not.

Pitfalls

• Choosing the tolerance after seeing the data.
• Treating any ratio near 1.6 as evidence.

Where to start reading

• Misconceptions about the Golden Ratio (George Markowsky, College Mathematics Journal, 1992)
• The Golden Ratio (Mario Livio)

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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