I would imagine that the area increases significantly, a less extreme example of what they say about fractal coastlines theoretically being able to have a perimeter of infinite length.
Comment on Is land inclination included in area calculation?
geogle@lemmy.world 3 months ago
No. It’s a flat approximation. The short answer is that once you take account for topography, your answer will always grow with surface resolution, and thus the actual surface area of rough topography is undefined.
niktemadur@lemmy.world 2 months ago
Dultas@lemmy.world 2 months ago
The Gabriel’s horn / painter’s paradox is a good one too.
SLVRDRGN@lemmy.world 2 months ago
jvw@lemmy.blahaj.zone 2 months ago
Congratulations! You just uncovered the premise of Cantor’s diagonal argument , which demonstrates this very thing: that there are an infinite number of infinite sets, each of a different size.
Also for some reason I can’t ever wrap my head around, this idea bothers some religious faith leaders enough to want the teaching of it banned in public schools. ¯\_(ツ)_/¯
angrystego@lemmy.world 2 months ago
And what about navigation, does it count the slopes in? Is the route actually longer than it says if you travel up and down mountains?
Silentiea@lemmy.blahaj.zone 2 months ago
It’s probably aware of them, but generally no. Most slippers for driving on are smooth enough to be pretty negligible unless you’re going hundreds of miles or more, in which case fives of miles won’t make much difference either.
But if you’re traveling by bike those small slopes may make some parts of the ride significantly more difficult or easier, and for cars may impact fuel efficiency in a way much more significant than just counting the extra distance traveled. So many navigation systems will still account for slope, even if they don’t necessarily acknowledge the length of your path as precisely as you may have hoped
Natanael@slrpnk.net 2 months ago
Not for distance, however when you start doing fuel calculations it gets counted in
Scrollone@feddit.it 3 months ago
It’s the same problem with defining coastlines. You can keep increasing the resolution and the coastline length will increase indefinitely.
Thavron@lemmy.ca 2 months ago
Ahh those fiddly little fjords.
geogle@lemmy.world 2 months ago
those fiddly atoms and quarks