The boundaries of states are so engrained in our minds that it can be hard to look at the earth without dividing it into political regions. But there are many other ways of looking at our planet. For example, what would the map of the world look like if each country only controlled all the land closer to its capital city than any other country's capital? Some might argue that it'd produce "mathematically perfect" borders.

Data visualization freelancer Jason Davies has had fun exploring these ideas using mathematics. With algorithms and the right datasets, he splits the planet into regions that contain only the land nearest a certain point — say, a capital city. Maps made with this technique are called Voronoi diagrams, and he's made maps of the world and the US that use the technique. The results are fascinating — and beautiful. The discrepancy between what land a country mathematically "should" own and the borders we know today is a result of everything from war and politics to geography and biology.

Davies' latest map leaves capitals behind. He's now divided the world into roughly 3,000 regions for all the medium and large airports in the world. Naturally, the wealthiest regions with high population densities have the greatest number of airports, but the Voronoi diagram shows just how much of the planet is sparsely served by air travel. If we have flyover states in the US, then there are clearly massive swaths of flyover land in the rest of the world. The most remote airport in the world, you ask? Mataveri International Airport on Easter Island, which is 1,617 miles (2,602km) from the next nearest airport.