Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

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

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: t-test: two-sample and paired · Confidence intervals for a mean · Descriptive statistics and box plots. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Ratios and measurement error; Comparing competing hypotheses
AA HL	Good fit	Ratios and measurement error; Descriptive statistics and confidence intervals
AI SL	Good fit	Ratios and measurement error; t-test of a mean against 1.618
AI HL	Good fit	Ratios and measurement error; Descriptive statistics and confidence intervals

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: choosing examples because they look golden; and ignoring measurement error. Say how each one affects your answer.

Use of mathematics (E)

SL: ratios and measurement error; t-test of a mean against 1.618; comparing competing hypotheses, each explained in your own words and carried out correctly.

HL adds: descriptive statistics and confidence intervals, each explained in your own words and carried out correctly.

How art & music explorations reach the top bands in general: Art, music & design IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

This idea already has HL mathematics in it: Descriptive statistics and confidence intervals. Make that the centre of the exploration and use it with full rigour.

See a complete IA, marked

Is a hanging chain a parabola? Comparing catenary and quadratic models (AA SL) is a complete art & music exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Ratios and measurement error, descriptive statistics and confidence intervals (HL), t-test of a mean against 1.618 (AI) and comparing competing hypotheses.

Where can I get data for this IA?

Measure 40+ examples from photographs with a scale (or official dimensions), estimating measurement error. Checked sources and tools: GeoGebra.

Turn this idea into your IA

The planner opens with “Is the golden ratio really everywhere? Testing a popular claim” filled in: the question, the maths and the data sources.

Plan this IA free

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Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · annotated exemplars, marked on every criterion