this post was submitted on 30 Jul 2024
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No Stupid Questions
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No such thing. Ask away!
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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.
I would imagine that the area increases significantly, a type of example of what they say about fractal coastlines theoretically being able to have a perimeter of infinite length.
EDIT: it just occurred to me that theoretically, if measuring area with a different scale, a country like Bhutan could claim to have as much surface area as... say Australia.
Or both are infinite, but since one fits inside the other, I'm getting into that weird mathematical study of infinities within infinities.
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)_/¯