niktemadur@lemmy.world to Ask Science@lemmy.worldEnglish · 1 month 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-up199arrow-down13
arrow-up196arrow-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 · 1 month agomessage-square14fedilink
minus-squaremumblerfish@lemmy.worldlinkfedilinkEnglisharrow-up41·edit-21 month 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-up20·1 month agoI’m going to start calling area “2-dimensional volume”
minus-squaremumblerfish@lemmy.worldlinkfedilinkEnglisharrow-up15·1 month agoOnly if you also call length “1-dimensional volume”.
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”.