Results 1 to 4 of 4

Math Help - how to divide an arc by...

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    103

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Narek View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    103

    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Narek View Post
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Divide
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 2nd 2010, 03:52 PM
  2. divide
    Posted in the Algebra Forum
    Replies: 4
    Last Post: January 16th 2009, 06:51 AM
  3. help divide
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 6th 2007, 12:37 PM
  4. Replies: 1
    Last Post: November 29th 2007, 06:17 AM
  5. Divide 2Pi into 4
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: June 27th 2005, 09:13 PM

Search Tags


/mathhelpforum @mathhelpforum