IA idea · Geometry, trigonometry & Voronoi diagrams

Do school catchment areas match the Voronoi diagram of the schools?

AI SLAI HL Solid Also in: Statistics

Research question

How closely do the official catchment areas of the primary schools in [my area] match the Voronoi cells of the schools, and where do they differ most?

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

Why it makes a good exploration

Many councils allocate places partly by distance, so catchments should look like Voronoi cells — but roads, rivers and politics get in the way. Comparing the two shows what pure geometry misses.

The mathematics you'll need

Voronoi diagrams from coordinates
Perpendicular bisectors and intersections
Areas of polygons (shoelace formula — explain it)
Percentage overlap between regions

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

Get school coordinates from OpenStreetMap and official catchment maps from your local council.

OpenStreetMap — Free map with exact coordinates of schools, hospitals, shops and stations; export or read off coordinates.
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

Explain how places are allocated locally.
Build the Voronoi diagram.
Overlay the official catchments.
Measure differences in area and identify causes.
Reflect on fairness and the limits of straight-line distance.

Pitfalls that cost marks

Using schools of different types (e.g., faith schools with different rules).
Not stating the map scale.
Assuming catchments are purely distance-based.

Showing personal engagement

Include your own primary school.
Interview a parent or teacher about admissions.
Suggest where a new school would reduce the largest cell.

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

Taking it further

Weight each school by capacity (a weighted Voronoi diagram) and see whether it matches better.

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).