What is a Radian?

A confusing item in beginning trigonometry is the radian.
In simple terms, an angle has measure of 1 radian when it slices a "piece of the pie" for which the curved edge is exactly the same length as the knife's slice.

In this animation, the angle of 1 radian shows the curved edge in red.
Naturally, an angle twice has big would have a measure of 2 radians, an angle half as big would measure .5 radian. Get the picture?

Could it be that "piece of the pie" relates to "pizza pie", and perhaps even to "piece of the π"

 

For more details about radians, click here.