2d shapes have an area and 3d shapes have a volume. Is it still called volume on 4d shapes? It shouldn’t be right?
In: Mathematics
When things are common, it’s okay to have specific words for specific situations. 2d and 3d shapes are fairly common, so we have different names for 2d and 3d situations.
Area vs. Volume
Circle vs. Sphere
But, mathematically, there are an infinite number of dimensions. So you can have 4d, 5d, 6d, with no end. But we can’t keep creating a new term for each level of dimension, so we just take one we’re already using and apply it.
So volume is still volume and sphere becomes n-sphere (where n is the level of dimensions it is).
Technically this is just linguistics. Volume is to area as 4D volume is to 3D volume. You could call 2d area volume if you wanted too, it would just make talking about these things confusing.
A forth dimension doesnt fit within our current understanding of how the universe works but if you want to try to then.
1D – linear distance aka length
2D – 1D of one plane * 1D of another plane
3D – 2D * 1D of third plane
4D – 3D * 2D
So basically, the previous dimension becomes the next dimensions side and 2-back becomes the edge.
If you think about it then a 4d shape contains each side as a 3d shape and each edge as a 2d shape (tesseract) rather than the 2d side and 1d edge like on a 3d shape.
Following this line of logic
5D – 4D sides, 3D edges
6D – 5D sides, 4D edges
In maths, it is sometimes called the “hypervolume”. This terminology is meant to be applied to things in dimensions greater than 3. This is related to other terms like “hypercube”, “hypersphere” and so on.
https://en.wiktionary.org/wiki/hypervolume
Uh… What 4D shapes? We live in a three dimensional world
Generally speaking, “area” refers to an outer surface, while “volume” refers to an interior space.
So a 4D interior space is still called a volume. The 4D object also has an outer (or enclosing) surface called an area.
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