Why would one assume that in the first place. The formula is meant for a perfect sphere. A perfect sphere has the lowest surface area possible for a spheroid. Any imperfection adds surface area.
But is a perfectly straight section of coastline infinite?
There was a fallacious explanation for this floating around a long time ago basically starting with a triangle and adding sides to the polygon 1 at a time, making the claim that it gets closer to being a circle each time but never actually becomes a perfect circle. It then made the claim that a perfect circle, therefore, is a polygon with infinite sides and as a result has infinite surface area. If someone is just… really gullible, gave it zero actual thought, and hasn’t taken middle school level math, it could have been convincing.
It hurts me to know that this is a real thing and plenty of people ate it up.
Ohhh, it’s like they got the first half of a riemann sum type explanation for curve integration, and started daydreaming halfway through
Or o fFinite Element triangulation
Slopini says it so I need to double check
The opposite even. The more imperfect the sphere the more surface area it has.
Coastline paradox, now in 3D!
Thats what i had in mind yep :3
Really depends on the imperfections
You can hand-craft imperfections to make the surface infinite, but you can also keep it constant or add very little
