IA idea · Geometry, trigonometry & Voronoi diagrams

Where should my town put its next defibrillator? A Voronoi analysis

AI SLAI HL Solid Also in: Health & biology

Research question

Using a Voronoi diagram of the existing public defibrillators in [my town], where is the point furthest from all of them, and is that the best place for a new one once population and access are considered?

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

Why it makes a good exploration

Survival after cardiac arrest drops quickly with every minute before defibrillation, so distance really matters. The largest-empty-circle method gives a precise answer — and the real-world objections to it give you outstanding Reflection.

The mathematics you'll need

Perpendicular bisectors: midpoint, gradient, perpendicular gradient, equation
Voronoi cells and vertices
Vertices as circumcentres; the largest empty circle
Distance formula and scale conversions
HL: incremental algorithm when a site is added

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

Locate defibrillators from your town's public register or OpenStreetMap (tag emergency=defibrillator); overlay a grid with a known scale.

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 why the problem matters and state the aim.
Set up coordinates and scale; tabulate sites.
Show one perpendicular bisector in full; tabulate the rest.
Construct the diagram and find the vertex furthest from its sites.
Critique the proposed site (roads, rivers, where people are) and propose an improved one.

Pitfalls that cost marks

Repeating identical bisector calculations — show one, tabulate the rest.
A diagram with no scale or axes.
Treating straight-line distance as travel distance without comment.

Showing personal engagement

Walk the proposed route and time it.
Talk to someone who manages first-aid provision locally.
Compare the result with population density data.

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

Taking it further

Recompute with taxicab distance for a grid-like town, or weight sites by opening hours (some are inside buildings that close).

See it done

Our annotated exemplar Where should our town put its next defibrillator? A Voronoi analysis (AI SL) explores a question like this one, with an examiner's comment on every criterion.

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).