It is well-known that it is impossible to trisect an arbitrary angle using only ruler and compass (this has been proven by P. L. Wantzel (1836)). However, elegant approximate methods, which offer sufficient accuracy for a reasonable constructing effort, have attracted much attention in the scientific community. Our method for approximate angle trisection is presented in Fig.1.
Fig.1
Let 
be the given angle to be trisected. Draw the bisector
, with 
.
Construct point 
on the segment 
such that 
. Construct point 
on the extension of line 
such that 
.
Construct point 
on the extension of line
such that 
. Draw a circle 
with center at
and radius 
. Draw a line perpendicular to the line
through point 
(or equivalently
a bisector of 
) which intersects
at point 
. Draw the line 
which intersects 
at point 
.
Now 
is an approximate trisection of 
.
In Fig.2 is shown the relative error for 
.
Table1 shows some numeric results of the presented trisection.
See also:
Avni Pllana "Angle Trisection using Limacon of Pascal" http://trisectlimacon.webs.com/