- #1
Opus_723
- 178
- 3
This isn't a homework question, but I'm having trouble understanding something about rotations conceptually. While reading about the Euler Identity online, I keep running into a few things that I can't wrap my head around and never come with an explanation.
Here are the concepts I can't understand:
A half-turn is the square of a quarter turn.
Rotations cannot be added, only multiplied.
Why is this? Intuitively, if I'm thinking about rotating by a quarter turn, then another quarter turn, I add them together to get a half turn. Instead, it appears I have to multiply the quarter turn by itself. I don't understand this.
pi equals 2(pi/2), not (pi^2)/4
Basically, I keep running across descriptions of rotations as exponential growth, whereas all I can see when looking at them is linear growth. How are rotations exponential?
Here are the concepts I can't understand:
A half-turn is the square of a quarter turn.
Rotations cannot be added, only multiplied.
Why is this? Intuitively, if I'm thinking about rotating by a quarter turn, then another quarter turn, I add them together to get a half turn. Instead, it appears I have to multiply the quarter turn by itself. I don't understand this.
pi equals 2(pi/2), not (pi^2)/4
Basically, I keep running across descriptions of rotations as exponential growth, whereas all I can see when looking at them is linear growth. How are rotations exponential?