### Trisect?

An idea for trisecting an angle. Take an arbritrary angle *BOC.* Let *OA* be the bisector
of the angle. Draw a circle of arbitrary radius with *O* as center. Here the circle passes
through *A, B* and *C.* Mark off three equal chords on that circle: *AD, DE,* and
*EF.* Draw *FG* parallel to *AO,* and let *G* be that point where that line
intersects *OB.* Draw the circle with center *O* and radius *OG.*. Now mark off
three equal chords on that circle, each equal to the previous chords: *HI, IJ,* and *JK.*
Then, for small angles, it looks like *K* = *G.* If *K* did equal *G*, then
*OI* and *OJ* would trisect angle *AOB,* hence *OJ* would be one of the
trisectors of *BOC.* Unfortunately, *K* is never equal to *G.* So this proposed
method for trisecting angles doesn't work.
It was proved in the 19th century that angles cannot be trisected with the Euclidean tools of
straightedge and compass.

This page:
May, 1999

David E. Joyce

Department of Mathematics and Computer Science

Clark University

Worcester, MA 01610

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