During the Crimean War, Florence Nightingale gathered the deaths of British soldiers, month by month, and drew each month as a slice of a disc. The choice remains of how the slice grows with the number.
The question
Should a number twice as large get a radius twice as long?
What you do Make the second number grow, from 1 to 4 times the first. On the left, the drawing of the first version (the radius follows the number); on the right, the corrected version (the area follows the number).
Without JavaScript, here are the animation’s data.
| The second number is | Area seen, if the radius follows the number | Area seen, if the area follows the number |
|---|---|---|
| the same as the first | ×1 | ×1 |
| twice the first | ×4 | ×2 |
| three times the first | ×9 | ×3 |
| four times the first | ×16 | ×4 |
The area of a slice of a disc is proportional to the square of its radius: doubling the radius multiplies the area by four. The numbers in the animation are examples, not Nightingale’s figures.
The takeaway The eye compares areas. If the radius follows the number, a number twice as large looks four times as large. To avoid misleading, the area must follow the number.
Sources 2
Small, Hugh, “Florence Nightingale’s Statistical Diagrams”, University of York, Department of Mathematics, description of the diagrams (“bat’s wing”, then “wedges”).
The length of the radial line in each month is proportional to the death rate, […] Florence recognised this error and inserted an erratum slip, but then replaced this diagram in later documents (nos. 3, 4, and 5 listed above) with what I will call the "wedges" diagram. […] In this diagram, Nightingale resolved the problem of the "bat's wing" by using areas to represent the variation in the death rate, instead of the length of radial lines.
Open access open the source · checked on 9 September 2026
Science Museum (Londres), “Florence Nightingale: The Pioneer Statistician”, section “The Crimean war”, then “An analytical approach to medical care”, then “Nightingale’s polar area diagram”.
The Crimean War (1853–6) was the first high-technology conflict of the modern age […] Nightingale set about collecting statistics in Crimea. She treated this activity—counting the number of soldiers killed, injured or diseased […] In her diagram, each wedge represented a month, and the area of the wedge showed the number of soldiers who had died that month.
Open access open the source · checked on 25 October 2026