Trisection by Sliding a Line

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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 .

Contributed by: Izidor Hafner (July 2012)
Open content licensed under CC BY-NC-SA



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.


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

[2] J. J. O'Connor and E. F. Robertson. "Trisecting an Angle." (Jun 21, 2012)

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