IA idea · Geometry, trigonometry & Voronoi diagrams

Which airport is really closest? Voronoi diagrams on a curved Earth

AI SLAI HL Ambitious Also in: Networks & graphs

Research question

How does a Voronoi diagram of major European airports drawn on a flat map differ from one using great-circle distances, and which towns change their nearest airport?

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

Why it makes a good exploration

Flat maps distort distance, so a Voronoi diagram drawn on one can give the wrong answer. Comparing flat and great-circle versions with real airport coordinates is a sophisticated, original twist on an AI topic.

The mathematics you'll need

Voronoi diagrams from coordinates
Latitude and longitude; map projection distortion
Great-circle distance with the haversine formula (new — explain it)
Testing border towns

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

Airport latitudes and longitudes from OpenFlights.

OpenFlights data — Airports (with latitude/longitude) and airline routes as CSV.
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

Choose 10–15 major airports and justify the choice.
Build the flat-map diagram.
Compute great-circle distances for towns near cell boundaries.
Identify towns whose nearest airport changes.
Reflect: travel time, cost and flight availability matter more than distance.

Pitfalls that cost marks

Treating degrees of longitude as equal distances at every latitude.
Using the haversine formula without explanation.
Too many airports to handle clearly.

Showing personal engagement

Include your home airport.
Check a border town you know.
Compare with actual flight availability from each airport.

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

Taking it further

Construct a spherical Voronoi boundary between two airports (a great circle) and compare it with the flat bisector.

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).