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For example on wikipedia for Switzerland it says the country has an area of 41,285 km². Does this take into account that a lot of that area is actually angled at a steep inclination, thus the actual surface area is in effect larger than what you would expect when looking onto a map in satellite view?
It's not, but I love the idea that it could be. You just know some of those megalomaniac dictators would be piling up fake Hills to make their country bigger. Turkmenistan would have giant Towers of dirt everywhere.
Due to the fractal nature of geometery, all they would have to do is use more fine-grained measurements. :)
Lets now measure all coastlines with the minimum increment possible, the planck length.
That would work for the perimeter, but not for the area.
It works exactly the same!
edit: With the assumption that we now measure inclines of course. If measuring area of the flattened overhead projection (the current normal way) we don't get fractal effect.
If I go over our parking lot with a 1m^2 granularity, I get 100m^2. If I go with 1cm^2 granularity, I get 110m^2 because I catch the sides of the curbs, potholes, etc.
https://demonstrations.wolfram.com/3DSnowflakeFractals/
I interpreted your reply to njm1314 as meaning "we don't need to measure inclination to cheat, we can do that by simply increasing our precision"
I see! Then I understand your response. :)
Fractals are self-replicating while surface area or coastline of a country are inherently finite. You could very accurately measure the surface area, but there's no reason to do that.
If you're measuring surface area it would.
Do you think the holes left by digging the dirt would also count as increased area? Because it feels like it'd be a 2 for one deal
Absolutely!
Oh man, holey cheese has one heck of a surface area doesn't it.
Depends on the thickness of the slice.
Eff that and their primitive math: I want to see the Vatican truck in gravel of precisely the size of the increment, to become THE LARGEST COUNTRY ON EARTH, MUAH HA HAH!