Is the golden ratio really everywhere? Testing a popular claim

AI SLAI HLAA SLAA HL Solid Also in: Statistics

Research question

Do the width-to-height ratios of [a claimed example, e.g. credit cards, famous paintings or building façades] cluster significantly closer to 1.618 than to other simple ratios such as 1.5 or √2?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

The golden ratio is the most over-used IA context, and most claims are never tested. Making the test the point of the IA — with measurement error and a proper statistical test — turns a cliché into a sceptical investigation.

The mathematics you'll need

Ratios and measurement error
Descriptive statistics and confidence intervals (HL)
t-test of a mean against 1.618 (AI)
Comparing competing hypotheses

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Measure 40+ examples from photographs with a scale (or official dimensions), estimating measurement error.

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

State the claim and where it comes from.
Define exactly what you measure.
Estimate measurement error.
Test the mean ratio against 1.618 and alternatives.
Reflect on confirmation bias in golden-ratio claims.

Pitfalls that cost marks

Choosing examples because they look golden.
Ignoring measurement error.
Declaring a match within ±10%.

Showing personal engagement

Test a claim you read or were taught.
Survey people's preferred rectangle and test that too.
Explain why the myth persists.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Run a preference experiment (people choose the most pleasing rectangle) and test whether choices cluster at 1.618.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).