Lets consider an arc which is part of a circle. using geometry, how can we divide this arc into (for instance) 3 equal parts????
What if the arc is not part of a circle but (for instance) an ellipse?
Thanks in advance
You only can bisect an angle by a construction using compass and straight edge.
But you can get $\displaystyle \frac13$ of an angle by using a geometric serie:
Since $\displaystyle \sum_1^\infty\left((-1)^{n+1} \cdot \left(\frac12\right)^n\right) = \dfrac13$
Apply this serie as a construction: Bisect the angle, bisect the half angle and subtract, bisect the quarter angle and add, ...
After 5 steps you have reached $\displaystyle \frac{11}{32}$ of the angle. If you need it more acurate then you have to perform some more steps.
A general remark:
1. I didn't divide an arc but an angle. Of course with this method you divide the arc of a circle too. I'm quite certain that this method will not work with ellipses or other curves.
2. You are looking for a geometrical method (see your first post). But I've never heard of a (geometrical) construction which yields a part of an arc. So sorry, but I can't help you any more.