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this post was submitted on 25 Jul 2024
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Say you have a smooth shape like: ███ That has a nice and simple area and surface area. But if you take a chunk out of it: █▂█ you now have less area, but surface area is the same plus those two new vertical walls - so it has increased. That is basically what roughing up the surface does. Might also do some deformation and add some peaks as well though far less than the material removed.
This all leads into the coastline paradox and fractal patterns which show that you can have a finite volume surrounded by an infinite surface area. Here are some interesting videos on the topic: https://www.youtube.com/watch?v=AD4vPNBSrKY https://www.youtube.com/watch?v=I_rw-AJqpCM https://www.youtube.com/watch?v=gB9n2gHsHN4 https://www.youtube.com/watch?v=3s7h2MHQtxc
I'm so geeked out right now, I can't even tell you. Thank you human, for these lovely videos. I actually have never heard of any of this outside of fractals, and even then I just know of them. When I was in school I got a taste of discrete mathematics, and nothing alive can signal how little you know than getting even a taste of this stuff. It's absolutely brain tingling, even if some of that tingle is pain in my case. Hahaha! I love it though, and I thank you for the explanation and these. Off to watch!