Talk:Geometry/Angles

I've been looking over the Geometry "pages" and I saw this Angles "page." The diagrams are good, but the article needs more work as of May 2, 2004. The written discussion could be much improved.

Angles AREN'T really the intersection of 2 rays
So after my second year of teaching HS Geometry, I've come to believe that teaching angles are the intersection of 2 rays is misleading and incorrect. The "angle", as traditionally drawn, is a shorthand, or a representation for a unit of rotational measurement. But it is the ROTATION that is primary, not the Angle Diagram, as we usually see.

Let's go back to the foundations of measurement. In the measurement world, there are two parallel universes: Rotational measurement and Linear Measurement. Linear measurement is measurement of displacement from a starting location. You start here, you move for a bit, and now you are 10 meters away. In Physics, velocity, acceleration, momentum, and position are all measurements that live in the "Linear" world.

In the Rotational World, there is a completely parallel universe. We have Rotational Velocity, Rotational Acceleration, Rotational Momentum, and it is all based on an underlying measurement: Rotational Position.

'''Angles are a measurement of Rotational Position. They answer the question: How far did something turn? '''

In my experience, teaching young students that angles are the intersection of two lines does not teach the true nature of an angle. I have had much more success teaching the concept of rotational measurement. Once that concept is understood, we can back down to the traditional representation, shown by two rays that share an endpoint. But until students understand the concept of rotation, the diagram involving rays simply confuses them.