How can you divide an angle into 3 equal angles? You may only use a straightedge and a compass to achieve this.

(This means : You have an angle A, you divide Angle A into 3 Angles B,C,D. And B=C=D=A/3)

Note: vohonam clarified that the problem actually only gives you a straightedge, not a ruler.

For what it's worth,

Draw an arc centered on angle A
Set the compass to a very short arc
Place the point of the compass on the intersection of the first arc with one ray of A
Mark off the length of the short arc on the first arc
Mark a second short arc off the end of the first, and a third off the second
If the third short arc doesn't exactly intersect the other ray of A, adjust your compass and try again.

When the three small arcs exactly extend along the first arc from ray to ray, you have the points through which you can now draw your trisecting lines.

There may or may not be a more formal way to solve this, but with a sharp pencil lead, this is as accurate a method as any.

Posted by Bryan on 2003-04-03 13:15:34