askchapo

NYC pop 8.468 million ~ 10,500,320 acres

us pop = 331.9 million ~ 411,556,000 acres

world pop = 8.1 billion ~ 10,044,000,000 acres

using .5 hectare estimate

This does not allow for any land degradation such as soil erosion, and it assumes adequate water supplies

That's really the problem imo, not space. Geometry is easy. It's all the limited reagents in the formula for feeding millions that's the problem.

It is also worth noting that of that 900 million acres, only a portion of it goes towards food for humans or livestock. Most of the corn and soybeans grown are used industrially for ethanol, lubricants, acids, starches, and rubber. We also grow things like tobacco, medicines, and cotton, which may be needed, but are not food. A significant portion of corn is also traded as a currency "commodity crop" in a market I don't understand at all.

If I recall correctly, roughly 40% of farmland is dedicated to food production for livestock, and 2% is dedicated to food for direct human consumption. So assuming you already have all necessities, and only need food without any change to an average american diet, we may need as little as 1.05 acres per person, following your math.

In modern time, we trade some space efficiency for automation efficiency, especially in the United States. Midwest USA agricultural production as an example, can feed ~1 acre per person, meat production included, and requires moderate energy input, and very little labor. But it's very possible to shrink that to ~0.1 acre per person, if you're willing to put more labor and capital investment into it, as well as changing people's diets. It just kind of depends on what you out of food production.

death rides a pale harvester combine

and since it reminded me, here's an excerpt from Terry Pratchett's Night Watch

Vimes climbed back up the barricade. The city beyond was dark again, with only the occasional removed of light from a shuttered window. By comparison the streets of the Republic were ablaze. In a few hours the shops out there were expecting deliveries, and they weren't going to arrive. The government couldn't sit this one out. A city like Ankh-Morpork was only two meals away from chaos at the best of times. Every day, maybe a hundred cows died for Ankh-Morpork. So did a flock of sheep and a herd of pigs and the gods alone knew how many ducks, chickens and geese. Flour? He'd heard it was eighty tons, and about the same amount of potatoes and maybe twenty tons of herring. He didn't particularly want to know this kind of thing, but once you started having to sort out the everlasting traffic problem these were facts that got handed to you. Every day, forty thousand eggs were laid for the city. Every day, hundreds, thousands of carts and boats and barges converged on the city with fish and honey and oysters and olives and eels and lobsters. And then think of the horses dragging this stuff, and the windmills . . . and the wool coming in, too, every day, the cloth, the tobacco, the spices, the ore, the timber, the cheese, the coal, the fat, the tallow, the hay EVERY DAMN DAY. . . And that was now. Back home, the city was twice as big . . . Against the dark screen of night, Vimes had a vision of Ankh-Morpork. It wasn't a city, it was a process, a weight on the world that distorted the land for hundreds of miles around. People who'd never see it in their whole life nevertheless spent their life working for it. Thousands and thousands of green acres were part of it, forests were part of it. It drew in and consumed . . .

. . . and gave back the dung from its pens and the soot from its chimneys, and steel, and saucepans, and all the tools by which its food was made. And also clothes, and fashions and ideas and interesting vices, songs and knowledge and something which, if looked at in the right light, was called civilization. That's what civilization meant. It meant the city. Was anyone else out there thinking about this? A lot of the stuff came in through the Onion Gate and the Shambling Gate, both now Republican and solidly locked. There'd be a military picket on them, surely. Right now, there were carts on the way that'd find those gates closed to them. Yet no matter what the politics, eggs hatch and milk sours and herds of driven animals need penning and watering and where was that going to happen? Would the military sort it out? Well, would they? While the carts rumbled up, and then were hemmed in by the carts behind, and the pigs escaped and the cattle herds wandered off? Was anyone important thinking about this? Suddenly the machine was wobbling, but Winder and his cronies didn't think about the machine, they thought about money. Meat and drink came from servants. They happened. Vetinari, Vimes realized, thought about this sort of thing all the time. The Ankh-Morpork back home was twice as big and four times as vulnerable. He wouldn't have let something like this happen. Little wheels must spin so that the machine can turn, he'd say.