ABSTRACT
This chapter begins with a review of radians and ends with a proof about “mystic hexagons.” Radians measure the openness of an angle in terms of an arc length, measured in units of a circle’s radius. As opposed to degree measure, radian measure nicely connects units of measure with the mental action of rotating. It also makes geometric theorems about chords and arcs that subtend angles more intuitive (e.g., the two chords theorem). Line segments can also subtend angles, but then their relation to angle measure is much more complicated. Investigating the connection between angle measure and subtending segments leads to Pascal’s theorem about mystic hexagons. The theorem is surprisingly simple, but proofs can get very complicated. A focus on the mental actions that undergird angle measure suggests a relatively simple proof.
