This Demonstration shows how to trisect an angle by sliding a line. Adjust the angle to trisect, , and then move point so that the point is on the line . The point is chosen so that is twice . The angle is a third of the angle .

Let . Assume the line is parallel to , is perpendicular to , and . If the point is on the line , and , then triangles and are isosceles. The angles and are equal and are equal to , but their sum equals . So .

The problem goes back to ancient Greece, with contributions by Hippocrates, Archimedes, and Pappus.

References

[1] P. Berloquin, The Garden of the Sphinx, New York: Scribner's, 1985 p. 179.