Rotation group SO(3)
So imagine you have a toy ball that you can spin around any way you want. This ball has a special property that it always looks the same no matter how you rotate it. This is called symmetry.
Now, there are many different ways you can spin this ball around. You can spin it in a circle like a top, or you can tilt it to the side and spin it that way. All of these different ways are called rotations.
The rotation group so(3) is a group of all the different possible rotations you can do with this ball. It's like a big club that includes all the possible ways you can spin the ball and still have it look the same.
The "so(3)" part of the name is just a fancy way of saying that this group includes rotations in three-dimensional space (which is where our toy ball exists).
So, the rotation group so(3) is just a big group of all the different ways you can spin a toy ball around and still have it look the same. Pretty cool, huh?
Now, there are many different ways you can spin this ball around. You can spin it in a circle like a top, or you can tilt it to the side and spin it that way. All of these different ways are called rotations.
The rotation group so(3) is a group of all the different possible rotations you can do with this ball. It's like a big club that includes all the possible ways you can spin the ball and still have it look the same.
The "so(3)" part of the name is just a fancy way of saying that this group includes rotations in three-dimensional space (which is where our toy ball exists).
So, the rotation group so(3) is just a big group of all the different ways you can spin a toy ball around and still have it look the same. Pretty cool, huh?