Angle Trisection Method by Archimedes

Explanation and Instructions

Line

is parallel to line

and line

is perpendicular to line

Circle

is constructed with radius

Points

and

are marked on a straightedge so that

The straightedge is aligned with point

while point

slides freely along line

To use the applet, drag point

until point

lies on circle

The measure of

should be three times the measure of

that is

Slide point

along line

to change the measure of angle

and repeat the process. This method can be proven through the use of isosceles triangles

and

Let

Then

and

Therefore,