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

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

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

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.

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

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.

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.

Taking it further

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