niktemadur@lemmy.world to Ask Science@lemmy.worldEnglish · 11 hours agoIf 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?message-squaremessage-square14fedilinkarrow-up174arrow-down12
arrow-up172arrow-down1message-squareIf 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 to Ask Science@lemmy.worldEnglish · 11 hours agomessage-square14fedilink
minus-squaremumblerfish@lemmy.worldlinkfedilinkEnglisharrow-up28·edit-211 hours agoYou’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]
minus-squareinsufferableninja@lemdro.idlinkfedilinkEnglisharrow-up13·10 hours agoI’m going to start calling area “2-dimensional volume”
minus-squaremumblerfish@lemmy.worldlinkfedilinkEnglisharrow-up10·10 hours agoOnly if you also call length “1-dimensional volume”.
minus-squareNotyou@sopuli.xyzlinkfedilinkEnglisharrow-up6·9 hours agoWhat happens if I turn the dimensional volume up to 11?
minus-squareironhydroxide@sh.itjust.workslinkfedilinkEnglisharrow-up5·9 hours agoWell if it’s in 1-dimensional space, then you have a line the length of 11 units.
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
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.