The 180 deg rotation indicates multiplying by negatives. It’s a good analogy to represent change to the opposite side. Which multiplying with negatives does, the number goes from one side of 0 on the number line to the other side.
I think the problem with this example is, while it provides a simple/visual thing to help people wrap their head around the idea of it, it still doesn’t really explain it.
When you turn around, you are spinning around a central point, in a circular motion, and when you have a circle, you will always end up back at the start. You start at 0°, and if you keep adding degrees, eventually you will hit 365°, and one degree more puts you back to 0° off from where you started. You do not have to reverse direction to get back to 0°
But with negative numbers you’re trying to explain a line, and that line goes in both directions infinitely. There is no point on the positive side of the line where you get teleported back to 0. You start at 0, keep adding numbers, and it’s going to keep going down that line forever until you start subtracting.
The problem is usually more about the person not understanding what a negative number actually represents. They just think of them as regular numbers that happen to exist on the other side of 0 on the number line. So multiplying by a negative number gets treated the same as multiplying by a positive, just with a little dash next to the result.
The 180 deg rotation indicates multiplying by negatives. It’s a good analogy to represent change to the opposite side. Which multiplying with negatives does, the number goes from one side of 0 on the number line to the other side.
It was used in my. complex numbers class - multiply by i means rotate 90 degrees on complex plane
and multiplying by i twice means you rotate 90 degrees twice. So 180 degrees. Multiplying by i twice means multiplying by i^2 = -1.
So multiplying by -1 is a rotation by 180 degrees
I think the problem with this example is, while it provides a simple/visual thing to help people wrap their head around the idea of it, it still doesn’t really explain it.
When you turn around, you are spinning around a central point, in a circular motion, and when you have a circle, you will always end up back at the start. You start at 0°, and if you keep adding degrees, eventually you will hit 365°, and one degree more puts you back to 0° off from where you started. You do not have to reverse direction to get back to 0°
But with negative numbers you’re trying to explain a line, and that line goes in both directions infinitely. There is no point on the positive side of the line where you get teleported back to 0. You start at 0, keep adding numbers, and it’s going to keep going down that line forever until you start subtracting.
The problem is usually more about the person not understanding what a negative number actually represents. They just think of them as regular numbers that happen to exist on the other side of 0 on the number line. So multiplying by a negative number gets treated the same as multiplying by a positive, just with a little dash next to the result.