The most circular country, with a roundness index of 0.934 (a perfectly circular country would have a roundness index of 1), is Sierra Leone. The next four, in order, and showing their respective roundness indices, are Nauru (0.923), Zimbabwe (0.915), The Vatican (0.908) and Poland (0.903).

The idea of measuring ‘roundness’ of countries was prompted by an earlier series of estimates of country ‘rectangularness’ carried out by David Barry, an Australian geo-statistician, in 2016. Barry wrote an algorithm to find the optimum rectangles to fit country borders using the country shapefiles from “Natural Earth” - a public domain map dataset available at 1:10m, 1:50m, and 1:110 million scales which, when used with GIS (Geographic Information Systems) software, can encode geographical information into a computer file.

A short time later in 2016, an Argentinian mathematician, Gonzalo Ciruelos, carried out a very similar analysis of country shapes using a different algorithm to find the world's roundest countries. Like David Barry he listed all the world's countries, but in this case in their order of roundness. In each of the approaches, 'optimum rectangularity' and ‘optimum roundness’ is the maximum percentage overlap of a country outline with, respectively, a rectangle and circle of the closest same area.

These studies are quintessentially the pursuit of trivia, as the outputs have no practical value, beyond their intellectual challenges.

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