2d shapes have an area and 3d shapes have a volume. Is it still called volume on 4d shapes? It shouldn’t be right?

Question

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

Answer 1

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).