Trapezoids, Octagons and Rhombuses have smooth edges, too... that doesn't make them round or like a circle. Maybe you should call this "Countries with the Smoothest Edges?" Though, I'm still not clear on what exactly you are measuring.
I would define "like a circle" or "round" using some kind of algortihm that awarded points for having the highest percentage of land being as close as possible to the geographic center of the country, as a ratio measured against the total area of the country, and would take points away for any large sharp edges. Not that that would be easy to come up with..
I figured out what you're measuring. I still think the title is misleading. I mean you could take a circle and completely flatten it out into a straight line... and the ratio would be perfect.. but the resulting shape would not be even remotely round and would look nothing at all like a circle. On the other hand you could have a country that was perfectly circular except the borders were full of grooves and shaped like a gear... and then it would not be on this quiz because it would have a very long coastline.
I don't understand your point with the flattened circle...if I'm correct the ratio is obtained dividing the perimeter of a circle with an area equivalent to that of the state, by the actual perimeter of the state (length of borders).
I think that a way to take into account your intuitive definition of "round country" would be to take the ratio between the radii of the largest inscribed circle and the smallest circumscribed one. In this way for example Lesotho would be less penalized for its highly irregular border.
I think that a way to take into account your intuitive definition of "round country" would be to take the ratio between the radii of the largest inscribed circle and the smallest circumscribed one. In this way for example Lesotho would be less penalized for its highly irregular border.