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

IA idea · Geometry, trigonometry & Voronoi diagrams

Who lives furthest from a supermarket? Food access with Voronoi diagrams

AI SLAI HL Solid Also in: Health & biology, Statistics

Research question

Using a Voronoi diagram of supermarkets in [my city], which areas are more than 1 km from the nearest supermarket, and how many residents live there?

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

Areas with poor access to fresh food affect health. Voronoi diagrams make it easy to see which supermarket serves which area — and where gaps are — turning geometry into a social question.

The mathematics you'll need

  • Voronoi construction and vertices
  • Distance from a point to its site
  • Largest empty circle
  • Estimating population in regions from census data

Where the data comes from

Supermarket locations from OpenStreetMap; population by area from your national statistics office.

  • OpenStreetMap — Free map with exact coordinates of schools, hospitals, shops and stations; export or read off coordinates.
  • Office for National Statistics (UK) — UK population, earnings, inflation, births and deaths time series.
  • GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

Real data for this idea

  1. Primary source: OpenStreetMap. Read off coordinates (right-click, “Show address”) or use Export for a small area. Licence: Open Database Licence: credit “© OpenStreetMap contributors”; data you build from it must be shared alike.
  2. Also useful: Office for National Statistics (UK): Population estimates. Use the UK mid-year estimates time series (year and total population). Licence: Open Government Licence v3.0: free to reuse with an acknowledgement.

OpenStreetMap is under the Open Database Licence: credit “© OpenStreetMap contributors”. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

  1. Define “supermarket” clearly (size, brands).
  2. Build the diagram and find poorly served areas.
  3. Estimate the population affected.
  4. Propose a new site and quantify the improvement.
  5. Reflect on car ownership, public transport and online delivery.

Pitfalls that cost marks

  • Inconsistent definition of which shops count.
  • Ignoring barriers such as rivers and motorways.
  • Population estimates without sources.

Showing personal engagement

  • Use your own neighbourhood.
  • Walk the longest route and time it.
  • Compare two neighbourhoods with different incomes.

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

Which course is it for?

CourseFitMaths to lean on
AA SLNot a natural fitThe core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HLNot a natural fitThe mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SLGood fitVoronoi construction and vertices; Distance from a point to its site
AI HLGood fitVoronoi construction and vertices; Distance from a point to its site

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: inconsistent definition of which shops count; and ignoring barriers such as rivers and motorways. Say how each one affects your answer.

Use of mathematics (E)

SL: voronoi construction and vertices; distance from a point to its site; largest empty circle; estimating population in regions from census data, each explained in your own words and carried out correctly.

How geometry & voronoi explorations reach the top bands in general: Geometry, trigonometry & Voronoi diagrams IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Use walking time along streets rather than straight-line distance for a few key areas and compare.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL geometry & voronoi exploration adds.

See a complete IA, marked

Where should our town put its next defibrillator? A Voronoi analysis (AI SL) is a complete geometry & voronoi exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

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

What mathematics does this IA use?

Voronoi construction and vertices, distance from a point to its site, largest empty circle and estimating population in regions from census data.

Where can I get data for this IA?

Supermarket locations from OpenStreetMap; population by area from your national statistics office. Checked sources and tools: OpenStreetMap, Office for National Statistics (UK) and GeoGebra.

Turn this idea into your IA

The planner opens with “Who lives furthest from a supermarket? Food access with Voronoi diagrams” filled in: the question, the maths and the data sources.

Plan this IA free

Your plan is kept in this browser. A free account keeps it with your drafts on any device: Join free · Sign in

Also: free IA self-check · A–E checklist (PDF) · have a draft? AI feedback or a review with Pete (€100)

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

Similar ideas

All geometry & voronoi ideas · AI SL ideas · AI HL ideas · All 239 IA ideas