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?

niktemadur@lemmy.world · 2 months ago

mumblerfish@lemmy.world · edit-2 2 months ago

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]

${isplaystyle V{n}(R)={rac {i ^{n/2}}{amma {igl (}{frac {n}{2}}+1{igr )}}}R^{n},}$

insufferableninja@lemdro.id · 2 months ago

I’m going to start calling area “2-dimensional volume”

mumblerfish@lemmy.world · 2 months ago

Only if you also call length “1-dimensional volume”.

Notyou@sopuli.xyz · 2 months ago

What happens if I turn the dimensional volume up to 11?

ironhydroxide@sh.itjust.works · 2 months ago

Well if it’s in 1-dimensional space, then you have a line the length of 11 units.

luciferofastora · 2 months ago

Well, you could just make 10 higher and make that the highest

threelonmusketeers@sh.itjust.works · 2 months ago

“But- but this one goes to 11.”