[cpitman]

For some reason Egypt has shown up as the most rectangular and now one of the most round countries. Goes back to how the average person's definition of these terms isn't capture by the metric. When I say a country is "rectangular" I'm thinking about straight lines and sharp corners. "Round" I guess should be the absence of corners?

[lmm]

Agreed. This feels like more a measure of how "blobby" a country is - the extent to which its territory is clustered around its centre. Countries that score lowest on this metric are island federations and long, thin countries like Chile or Western Sahara.

[gciruelos]

There's nothing wrong with that. A square is very "round" in the sense that it is very close to a circle in terms of shape, compared to all other possible polygons out there.

[emptybits]

> A square is very "round" in the sense that it is very close to a circle in terms of shape, compared to all other possible polygons out there.

Regular convex n-gons approach a circle in terms of shape as n increases. A square represents n=4. For any n>4, the polygon will be closer to a circle in terms of shape than a square, no?

ADDED: Right. Thank you for pulling my head out of abstract, regular convexness. IRL FTW. :-)

[sirclueless]

Yes, but you are only looking at regular N-gons, while the person you are responding to is considering all polygons.

Square countries are relatively close to being circular compared to the many highly irregular countries out there, not compared to other regular N-gons.

[Tideflat]

Many countries are irregular polygons like Chile. Thus a square is very close to a circle, relative to the other shapes.