- #1
pivoxa15
- 2,255
- 1
Homework Statement
Group of rotations of S^1 = SO(2)=S^1 conincidently
Group of rotations of S^2 = SO(3)
Group of rotations of S^3 = SO(4)
Correct?
The Attempt at a Solution
SO(3) is the group of all rotations in R^3 so it can rotate all elements of S^2 which is part of R^3. Although I can't show it rigorously.
Would it be enough to say since SO(3) consists of all rotations in R^3, it can offcouse rotate all elements having unit distance from the origin.
Similar argument made to S^1 and S^3.
Last edited: