What is the easiest way to trisect a line with simple construction ?

Question

What is the easiest way to trisect a line with simple construction ?

Answer 1

I can remember being taught one method in school.

From one end of the line you wish to trisect, draw another line whose length is easily divisible by three, but of a similar length, at an angle to it - at around 40 to 50 degrees or so.

Now mark the new line with two points which divide it into three sections.

Draw a line joining the free ends of both lines to form a triangle.

Now draw two lines, one from each of the two points on your second line, and parallel to the last line drawn (the one which completes the triangle) until they intersect the original line you want to trisect.

Those points of intersection will be at the one and two thirds points.

Answer 2

OK I got it!

Let the line to be trisected be called AB

Draw a straight line from one end A of the line to be trisected at an angle of 40-50 degrees (it doesn't matter). Keep this line a little longer than AB

Take a divider and measure off about one third of distance on the new line and set any three equidistant points D, E and F

AD = DE = EF

Join F to B

Draw lines parallel to BF from points E and D

The points where these parallel lines intersect AB divide AB in exactly three parts

Answer 3

To do a true geometrical trisection (i.e., with compass and straightedge) is impossible.  The previous poster has included a step in his method that requires measuring which is not allowed in a true geometrical construction.