If a 1D figure has length, a 2D figure has area, and a 3D figure has volume, are there names for what's inside 4D, 5D figures and so on?
If a 1D figure has length, a 2D figure has area, and a 3D figure has volume, are there names for what's inside 4D, 5D figures and so on?
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You'd just continue saying 'volume', alternatively 'k-dimensional volume' or 'volume of the n-dimensional object'. Like for spheres: https://en.m.wikipedia.org/wiki/Volume_of_an_n-ball
The n-dimensional volume of a Euclidean ball of radius R in n-dimensional Euclidean space is:[1]
I'm going to start calling area "2-dimensional volume"
Only if you also call length "1-dimensional volume".
What happens if I turn the dimensional volume up to 11?
Well if it's in 1-dimensional space, then you have a line the length of 11 units.
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