Vatican is entirely encircled in Rome, therefore any area outside Vatican is closer to Rome than the Vatican, yet if we look at them as point sources, as this map does, you see a lot of other area closer to Vatican.
- a difference metric between this coverage and the actual map (and country breakdown of same)
- a weighted version () with weights chosen to optimize the above distance metric.
The latter is in itself is a fun math problem -- the gradient on such an objective clearly exists (and the numerical gradient is fairly cheap). But can you prove anything about its structure? Is there a closed form that could be derived from the map information?
There’s an Observable version here if you want to see an implementation using d3-geo-voronoi: https://observablehq.com/@d3/world-airports-voronoi
In the US, the southwesternmost bit of Virginia is closer to 9 other state capitals than to Virginia's capital of Richmond (https://cardinalnews.org/2022/02/28/ewing-is-closer-to-nine-...). On a world scale these numbers can get quite large - it looks like 33 capitals are closer to Vladivostok than Moscow is (https://mathematica.stackexchange.com/questions/159041/how-m...).
Fun fact from this map, if I’m not mistaken, Greece is the only country touching three continents (Europe, Africa and Asia.
I keeps pretty much all its territory and it absorbs a significant chunk of the USA.
According to Wikipedia: Mongolia is approximately 1,564,116 sq km, while Russia is approximately 17,098,242 sq km, making Russia 993% larger than Mongolia.