IA idea · Geometry, trigonometry & Voronoi diagrams

Would a Voronoi diagram have pointed John Snow to the Broad Street pump?

AI SLAI HL Solid Also in: Health & biology, Statistics

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?

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

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

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

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.

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

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.

Taking it further

Build a network (graph) of streets and compute walking-distance cells, then compare with the Euclidean diagram.

Turn this idea into your IA

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