# Thread: how to divide an arc by...

1. ## how to divide an arc by...

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?

2. Originally Posted by Narek
Lets consider an arc which is part of a circle. using geometry, how can we divide this arc into (for instance) 3 equal parts????

...
You only can bisect an angle by a construction using compass and straight edge.

But you can get $\frac13$ of an angle by using a geometric serie:

Since $\sum_1^\infty\left((-1)^{n+1} \cdot \left(\frac12\right)^n\right) = \dfrac13$

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 $\frac{11}{32}$ of the angle. If you need it more acurate then you have to perform some more steps.

3. ## Thank you but I have more questions

Thank you my friend for helping me. Now 2 more questions are came up for me:

1- Is this works for all arcs from ellipse or other shapes?

2- what If I need 1/5 ? or 1/7?

Thank you again

4. Originally Posted by Narek
Thank you my friend for helping me. Now 2 more questions are came up for me:

1- Is this works for all arcs from ellipse or other shapes?

2- what If I need 1/5 ? or 1/7?

Thank you again
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.

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# how to divide an arc into 5 equal parts

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