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how many people could fit in a PDF?

i saw this tweet from Terrible Maps about the maximum size of a PDF, after SwiftOnSecurity quote-tweeted it about living in a country that fits in a PDF, and had an idea: "how many people could fit in a PDF"? so, i decided to do the math.

first, let's find the exact width and height. the Terrible Maps tweet say 381 by 381 kilometers, but i'd like to know if that's an exact or rounded figure.

i searched on search.w212.org for the maximum size, which led me to this link, which states that the maximum size is 15 million inches². conveniently, when converted to kilometers, that is exactly 381 kilometers, meaning that our previous figure was in fact correct.

the next question that must be answered is, of course, how much space does a person need? according to socialtables.com 6 square feet (about half a meter²) per person should suffice.

putting this altogether, we get the answer of ((145161 kilometers²) / (6 feet²)), or (fanfare intensifies) ... 260,416,666,666.6... can you guess the rest? people. at over a quarter trillion, this is sure to hold all of earth's population for good.

but, this isn't a very accurate figure. in my opinion, it would be better to look at other countries nearby for a baseline. take a look back at that Terrible Maps tweet. see, this hypothetical country is mostly in germany. some is in the czech republic, but we'll pretend that that land was ceded to this country, to make the math easier.

germany has 83.2 million citizens, with an area of 357,580 kilometers². plugging this in, we can see that germany has a population density of 232.6752055 people per kilometer².

applying that to our 381x381 kilometer² document-heaven, we get our final answer. it could fit 33,775,365 and a half people. guess someone will halfed to be left out get it?.