Take look at a map of Turkey and you’ll have to agree: it’s a curiously box-shaped country. Why is the wrong question. Like most international borders, Turkey’s are the result of geopolitical accident, not of aesthetic or geometric design. A more pertinent query: How rectangular is Turkey? Is it, perhaps, the most rectangular country in the world?

To answer that question, you’d have to find a dataset that minutely describes the borders of all countries on Earth and devise an algorithm that compares each country’s shape to an optimum rectangle with the same area.

That’s exactly what Australian geo-statistician David Barry did. His conclusion: Turkey is only the 15th most rectangular country in the world. The winner: Egypt.

Inevitably, one esoteric geographical question led to its opposite: What is the roundest country in the world? That one was answered by Gonzalo Ciruelos, an Argentinian mathematician. The top of that ranking is Sierra Leone.

As the winners in both categories indicate, Africa is a country of great diversity in geopolitical morphology. But the most curious country in either ranking is… the Vatican. As it turns out, the Papal State is both the 4th roundest and the 2nd most rectangular country in the world. How is that possible?

First, let’s have a closer look at the results. In Mr Barry’s definition, ‘optimum rectangularity’ is the maximum percentage overlap of a country with a rectangle of the same area.

He’s the first to admit that his algorithm may be inadequate for some countries with complex shapes (“Italy looks like the biggest country that might be wrong”), scattered geographies (e.g. Norway, because it includes Bouvet Island, a Norwegian dependency located between South Africa and Antarctica, freakishly far from the motherland) or locations on either side of the 180° longitude meridian (New Zealand, United States, Russia).

Also, the Natural Earth database includes small dependencies such as Scarborough Reef (1) as separate entries, which somewhat distorts a per-country ranking. Still, here goes:

Cutting through empty deserts, Egypt’s western and southern borders are completely straight—the Bir Tawil Trapezoid (2) is a notable but statistically insignificant exception. Combined with a fairly straight Mediterranean coastline in the north and its only slightly slanted Red Sea shore in the east, Egypt gets a ‘rectangularity’ score of 0.955 (out of 1), and the first place.

The Vatican’s actual borders are a lot more varied than this boxy rendition—perhaps because the database wasn’t built to reflect the delineation of the world’s smallest state in the greatest possible detail. That may explain why the geopolitical headquarters of the Catholic church manages to rank second in this list.

(For the balance of this interesting article please visit: https://bigthink.com/strange-maps/sierra-leone-is-the-worlds-roundest-country-and-egypt-the-squarest-one/)