How to measure angles on the spiral

Here's how we measure angles on the spiral.

Number wheel, figure 4
Figure 1

The green arrow in Figure 2 is like a clock hand. It turns counterclockwise in the direction of the red arrow.

The green arrow starts from the solid black line. When it's on that line, the angle is zero. If the arrow goes all the way around and returns to the solid black line, that would be one rotation. Right now the arrow has traveled one-eighth of the way around, so the angle is 1/8 rotation.

Normally people measure angles in degrees or radians, not rotations. So, if you prefer, you can call this angle "45 degrees" or "pi/4 radians" instead of "1/8 rotation," since all three phrases mean the same thing.

The reason I measure in rotations on this website is that it makes the spiral's arithmetic simpler and easier to understand.