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> shape’s volume dwindles to zero, while its surface area grows infinitely large I think it's easy to grok when you get it, but that's certainly counter-intuit
by betenoire 2y ago
> shape’s volume dwindles to zero, while its surface area grows infinitely large
I think it's easy to grok when you get it, but that's certainly counter-intuitive on the surface, no?
- emptiestplace 2y agoI won't say it isn't possible that someone might struggle with this—it's quite subjective, obviously—but I do think it's unlikely that anyone with a general understanding of both volume and surface area would struggle here. Even just comparing two consecutive iterations, I feel confident that any child who has learned the basic concepts would be able to reliably tell you which has more enclosed volume or surface area. I will happily concede that the part you quoted could be quite unintuitive without the context of the article or the animation included in it. :)
- benbayard 2y agoI think Gabriel's Horn is a great explanation of how this is counter-intuitive[1]. This is a shape which you could fill with a finite amount of water, say a gallon. Yet it would take an infinite amount of paint to paint the surface. Of course, part of the reason it's counter-intuitive is that there is no 0-thickness paint that exists. [1] https://en.wikipedia.org/wiki/Gabriel%27s_horn https://en.wikipedia.org/wiki/Gabriel%27s_horn