DEFINITELY NOT A COMMON SENSE PROBLEM
Geometry
Level
pending
Find the space diagonal of theoretical 4D cube.with side length 1.
Bonus:Generalize how to find a space diagonal of an n dimension cube.
The answer is 2.
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1 solution
The diagonal of a square is sqrt(2s^2)=sqrt 2 s.The space diagonal of a 3D cube is sqrt(2 (s^2)+s^2)=sqrt 3*s.The space diagonal of a 4D cube is sqrt((3s^2)+s^2)=sqrt 4 *s=2s(2x1=2).The general formula to find a space diagonal of an n dimensional cube is sqrt n *s(Very easy to prove ;just keep adding s^2 so each time you will have the same s and a sqrt n+1 ).