IA idea · Geometry, trigonometry & Voronoi diagrams
Would a Voronoi diagram have pointed John Snow to the Broad Street pump?
Research question
Using the digitised 1854 cholera data, what proportion of deaths lie in the Voronoi cell of the Broad Street pump, and is that proportion significantly higher than the cell's share of the area?
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Why it makes a good exploration
John Snow's map of the 1854 cholera outbreak is one of the founding moments of epidemiology — and Snow himself drew a boundary equivalent to a Voronoi cell around the pump. You can recreate and test his reasoning with the real coordinates.
The mathematics you'll need
- Voronoi diagrams from 13 pump coordinates
- Point-in-polygon counting
- Chi-squared goodness-of-fit (deaths vs area shares)
- Straight-line vs walking distance
Where the data comes from
Use the digitised coordinates of deaths and pumps from the HistData package (units of 100 m).
- John Snow's 1854 cholera data (HistData) — Coordinates of 578 cholera deaths and 13 water pumps around Broad Street, digitised from Snow's map (units of 100 m).
- GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.
A possible outline
- Tell the historical story briefly and state the aim.
- Build the pump Voronoi diagram.
- Count deaths per cell.
- Test whether deaths are proportional to area.
- Reflect on walking routes, the brewery and workhouse anomalies, and correlation vs causation.
Pitfalls that cost marks
- Retelling history at length instead of doing mathematics.
- Ignoring that deaths are stacked at addresses on the original map.
- Area proportions calculated inaccurately.
Showing personal engagement
- Explain the anomalies Snow found (people who did not die) with your data.
- Use walking distance along streets for a few cases.
- Relate to modern outbreak mapping.
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 | Good fit | Voronoi diagrams from 13 pump coordinates; Point-in-polygon counting |
| AI HL | Good fit | Voronoi diagrams from 13 pump coordinates; Point-in-polygon counting |
Level: Solid. Needs some independent work beyond class examples. 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: retelling history at length instead of doing mathematics; and ignoring that deaths are stacked at addresses on the original map. Say how each one affects your answer.
Use of mathematics (E)
SL: voronoi diagrams from 13 pump coordinates; point-in-polygon counting; chi-squared goodness-of-fit (deaths vs area shares); straight-line vs walking distance, 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
Build a network (graph) of streets and compute walking-distance cells, then compare with the Euclidean diagram.
Extending it for HL
Add an HL technique the question genuinely needs: what an HL geometry & voronoi exploration adds.
See a complete IA, marked
Where should our town put its next defibrillator? A Voronoi analysis (AI SL) 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 Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Voronoi diagrams from 13 pump coordinates, point-in-polygon counting, chi-squared goodness-of-fit (deaths vs area shares) and straight-line vs walking distance.
Where can I get data for this IA?
Use the digitised coordinates of deaths and pumps from the HistData package (units of 100 m). Checked sources and tools: John Snow's 1854 cholera data (HistData) and GeoGebra.
Turn this idea into your IA
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