Thread: 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?

Thanks in advance

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 of an angle by using a geometric serie:

Since

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 of the angle. If you need it more acurate then you have to perform some more steps.

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

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.