Trisecting an Angle

This is a simple straightedge and compass construction of a third part of an angle. In the illustration for Step Four, the angles DOC and OCD are equal, and they add up to the angle ODE. Angle ODE is equal to angle OED, and their sum is equal to the sum of DOC and FOE. Using algebra, it is easy to see that angle DOC is a trisection of angle FOE.
angle to be trisected Step One:
This is an acute angle AOB. If this angle can be trisected, the construction can generalize to any arbitrary angle.
drawing circle and line Step Two:
Set the compass to an arbitrary distance. The compass setting will not be changed throughout this construction. Using O as a center, draw a circle. Use the straightedge to extend the line OA to the left, and set the compass on the intersection of the circle and line OA, with the other point on the extended line.
move compass and ruler Step Three:
Hold the straightedge to the compass, and slide one end of the compass along the line OA, while the other end of the compass moves up the circle. Stop when the straightedge is aligned with the intersection of the circle and OB.
angle is trisected Step Four:
Mark point D on the circle with the compass. The angle DOC is exactly one third of the angle AOB.