Comment on Is land inclination included in area calculation?

geogle@lemmy.world ⁨1⁩ ⁨month⁩ ago

• Scrollone@feddit.it ⁨1⁩ ⁨month⁩ ago

  It’s the same problem with defining coastlines. You can keep increasing the resolution and the coastline length will increase indefinitely.

  source

  • Thavron@lemmy.ca ⁨1⁩ ⁨month⁩ ago

    Ahh those fiddly little fjords.

    source

    • geogle@lemmy.world ⁨1⁩ ⁨month⁩ ago

      those fiddly atoms and quarks

      source
• niktemadur@lemmy.world ⁨1⁩ ⁨month⁩ ago

  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.

  source

  • Dultas@lemmy.world ⁨1⁩ ⁨month⁩ ago

    The Gabriel’s horn / painter’s paradox is a good one too.

    source

    • SLVRDRGN@lemmy.world ⁨1⁩ ⁨month⁩ ago

      Never heard of it before, that’s another mind melter. How does the volume of the horn end up to neatly be pi ?? YouTube link I found.

      source
  • jvw@lemmy.blahaj.zone ⁨1⁩ ⁨month⁩ 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⁠)⁠_⁠/⁠¯

    source
• angrystego@lemmy.world ⁨1⁩ ⁨month⁩ 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?

  source

  • Silentiea@lemmy.blahaj.zone ⁨1⁩ ⁨month⁩ 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

    source
  • Natanael@slrpnk.net ⁨1⁩ ⁨month⁩ ago

    Not for distance, however when you start doing fuel calculations it gets counted in

    source