IA ideas library
Voronoi diagram and geometry IA ideas
Voronoi diagrams split a map into regions that are closest to each of a set of sites — hospitals, schools, phone masts, water pumps. They are in the AI course and make excellent IAs because the geometry (midpoints, gradients, perpendicular bisectors, circumcentres) is used to answer a real planning question: where should the next one go?
Geometry and trigonometry ideas outside Voronoi work too: measuring heights you cannot reach, modelling shapes in architecture, or checking claims about angles and proportions.
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
How geometry & voronoi explorations reach the top bands
Personal engagement (C)
Use a real place you know and a real decision. Build part of the diagram by hand (the perpendicular bisectors) before using software, and explain every choice of site and boundary.
Reflection (D)
Reflect on the gap between straight-line distance and real travel (roads, rivers, time), and on whether the answer would change the decision you started with.
Use of mathematics (E)
SL: Perpendicular bisectors found algebraically, the Voronoi diagram built and checked, and the largest empty circle or a toxic-waste-dump style question answered with calculation.
HL: Go beyond the standard construction: a weighted or taxicab variant, spherical distances, an optimisation over the region, or a proof of a property you use.
An HL version
Replace straight-line distance with a weighted, taxicab or great-circle distance and show how the regions change.
Geometry, trigonometry & Voronoi diagrams ideas (12)
- Where should my town put its next defibrillator? A Voronoi analysisAI SLAI HLSolid
- Do school catchment areas match the Voronoi diagram of the schools?AI SLAI HLSolid
- Who lives furthest from a supermarket? Food access with Voronoi diagramsAI SLAI HLSolid
- Voronoi diagrams in a grid city: Euclidean or taxicab distance?AI SLAI HLAA HLAmbitious
- Which airport is really closest? Voronoi diagrams on a curved EarthAI SLAI HLAmbitious
- Would a Voronoi diagram have pointed John Snow to the Broad Street pump?AI SLAI HLSolid
- Should bigger hospitals get bigger regions? Weighted Voronoi diagramsAI HLAI SLAmbitious
- Which method measures a building's height most accurately?AA SLAI SLAccessible
- Designing a working sundial for my latitudeAA SLAA HLAI SLAI HLSolid
- Why do flight paths curve on the map?AA SLAA HLAI SLAI HLAmbitious
- Modelling the sun's height from a stick's shadowAA SLAI SLAA HLAI HLAccessible
- Is a satellite dish really a parabola, and where is its focus?AA SLAA HLSolid
Also relevant (29)
- Which function best describes the arch of a famous bridge?AA SLAI SLAccessible
- Can you predict a tree's height from its trunk?AI SLAI HLAA SLSolid
- What is the best shape for a rain gutter?AA SLAI SLAA HLAI HLAccessible
- How big is my local lake? Estimating area with the trapezoidal ruleAI SLAI HLAA SLAA HLAccessible
- The lifeguard problem: what is the fastest route to a swimmer?AA SLAA HLAI SLAI HLSolid
- Will the sofa fit round the corner? The longest object through a corridorAA SLAA HLAI SLAI HLSolid
- Where is the best seat in the cinema?AA SLAA HLAI SLAI HLSolid
- How much is being near a station worth?AI SLAI HLAA SLSolid
- Where should a winger shoot from? Maximising the angle to goalAA SLAA HLAI SLAI HLSolid
- Where should a pool ball hit the cushion? The geometry of bank shotsAA SLAI SLAccessible
- What is the best tilt for a solar panel at my home?AA SLAI SLAA HLAI HLSolid
- How does the shape of the daylight curve change with latitude?AA SLAI SLAA HLAI HLAccessible
- How do doctors estimate your skin area? Comparing body-surface-area formulasAA SLAA HLAI SLAI HLSolid
- What is the shortest route to walk every corridor in my school?AI HLSolid
- What is the cheapest way to connect villages with fibre broadband?AI HLAI SLSolid
- How many flights does it take to get anywhere?AI HLAI SLAmbitious
- The product of a regular polygon's diagonalsAA HLAmbitious
- How long is a coastline? Measuring fractal dimensionAA SLAA HLAI SLAI HLSolid
- Symmetry in Islamic geometric art: which wallpaper groups appear?AA HLAA SLAmbitious
- How accurate is the perspective in a Renaissance painting?AA SLAI SLAA HLAI HLSolid
- Where should a shared mast go? Minimising total distance to villagesAA HLAI HLAA SLAmbitious
- Square or hexagonal? Packing tins into a boxAA SLAA HLAI SLSolid
- What is a 'random' chord? Bertrand's paradox simulatedAA HLAA SLSolid
- How wide is the river? Measuring a distance you can't crossAA SLAI SLAccessible
- How far can you see from the top of a hill?AA SLAI SLAA HLSolid
- How far off do you end up? Navigating a route by bearingsAA SLAI SLAccessible
- Measuring the area of an irregular field with trianglesAA SLAI SLAccessible
- Measuring the Earth with a stick and a partner schoolAA SLAI SLAA HLSolid
- The hidden angles of a hip roof: 3D trigonometryAA SLAI SLAA HLSolid
Frequently asked questions
Can AA students do a Voronoi IA?
Yes. Voronoi diagrams are only examined in AI, but the coordinate geometry they need (midpoints, gradients, perpendicular lines, distance) is familiar to AA students. Explain the new idea clearly and take it further, for example with weighted regions or a different distance measure.
How do I get coordinates for a Voronoi diagram?
Read them from OpenStreetMap or an online map with a scale, overlay a grid, and state your scale and origin. Real places make the IA personal; make sure your coordinates are accurate enough for the decision you are making.
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