Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

Make it yours, then agree it with your teacher.

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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

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.

Real data for this idea

Primary source: OpenFlights data: Airports and routes. airports.dat gives name, IATA code, latitude and longitude; routes.dat gives each route's source and destination airport. Licence: Open Database Licence. The routes file is a 2014 snapshot.

The OpenFlights routes file is a 2014 snapshot: treat it as historical and say so. Links checked October 2026; we link to the data and never copy it. More free data sets.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Not a natural fit	The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HL	Not a natural fit	The 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 SL	Fits — ambitious at SL	Voronoi diagrams from coordinates; Latitude and longitude; map projection distortion
AI HL	Good fit	Voronoi diagrams from coordinates; Latitude and longitude; map projection distortion

Level: Ambitious. Suits confident students; expect to learn some mathematics on your own. 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: treating degrees of longitude as equal distances at every latitude; and using the haversine formula without explanation. Say how each one affects your answer.

Use of mathematics (E)

SL: voronoi diagrams from coordinates; latitude and longitude; map projection distortion; great-circle distance with the haversine formula (new — explain it); testing border towns, 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

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

Extending it for HL

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

See a complete IA, marked

What is the quickest way to deliver a leaflet to every house on my estate? (AI HL) 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 Ambitious: it suits confident students, who should expect to learn some mathematics on their own.

What mathematics does this IA use?

Voronoi diagrams from coordinates, latitude and longitude; map projection distortion, great-circle distance with the haversine formula (new — explain it) and testing border towns.

Where can I get data for this IA?

Airport latitudes and longitudes from OpenFlights. Checked sources and tools: OpenFlights data and GeoGebra.

Turn this idea into your IA

The planner opens with “Which airport is really closest? Voronoi diagrams on a curved Earth” filled in: the question, the maths and the data sources.

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