>>4494536 (last)
Here I am going to side with the math teacher. You can count the angle around a circle at any scale you want. Some people say it's 2 * pi (pi = 3.14159) because that's the radius of a unit circle, so it relates the angles (in the "radians" measure) to the distance they subtend on the unit circle. In fact that's the convention in almost all mathematics.