The counties shaded blue are the 462 least densely populated counties of the nation. None of them have a population density greater than 7.4 people per square mile. In 65 of these counties, the density is less than one person per square mile.

The least-populated place in the United States is Alaska's Yukon-Koyukuk Census Area. At over 145,000 square miles, it's larger than New York, Pennsylvania, Maryland and Virginia -- combined. But it's home to only 5,547 people, for a population density of fewer than 4 people every 100 miles.

One other way to understand these extremes is to compare our 462 most sparsely populated counties with some of the most populated places in the United States. In the map below, I highlighted New York's Bronx and Queens counties in orange. Together they're home to 3.8 million people -- far more than the population of the blue counties.

None of this is terribly complicated or groundbreaking. We all know how population density works -- the country is made up of cities and rural areas, and there are way more people in the former than in the latter.

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But if it's easy enough to understand the concept in theory, it's even easier to lose track of how truly vast and unpopulated many of the country's rural areas are. This is especially true for those of us who live on the coasts, or in the eastern half of the country.

Geographically speaking, we are a nation of mountains, forests and farmland surrounding tiny islands of urbanity. These maps help put some of that in perspective.