Results 1 to 8 of 8
Like Tree3Thanks
  • 3 Post By Prove It

Math Help - Investigate Equality

  1. #1
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Question Investigate Equality

    Problem: Investigate following equality:

    \frac{2}{\pi }=\frac{\sqrt{2}}{2}   \frac{\sqrt{2+\sqrt{2}}}{2}   \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \text{...}

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16

    Re: Investigate Equality

    What is there to investigate? Do you want to prove the equality? Do you want to formulate a partial product and see if it converges?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Investigate Equality

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16

    Re: Investigate Equality

    My thorough investigation revealed that this is Vičte's formula. Now what?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Thumbs up Re: Investigate Equality

    Thanks a lot Vlasev, you are truly a good n efficient investigator...good to know the origin of the problem.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,329
    Thanks
    1244

    Re: Investigate Equality

    You can define a circle to be a regular polygon with an infinite number of sides. We can define \displaystyle \begin{align*} \pi \end{align*} as the circumference of a circle of diameter equal to 1 unit. Therefore, we can get an approximation for \displaystyle \begin{align*} \pi \end{align*} by evaluating the perimeter of said regular polygon.












    Some algebraic manipulation of this will give the result you are trying to prove.
    Thanks from MaxJasper, Vlasev and emakarov
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Re: Investigate Equality

    This explanation is truly enlightening. Thanks a lot ProveIt.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    16

    Re: Investigate Equality

    That's indeed a magnificent proof!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: December 17th 2011, 11:48 AM
  2. [SOLVED] Given a group how to investigate groups that are homomorphic to it
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: May 14th 2011, 04:29 PM
  3. Investigate the sequence?
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: January 23rd 2011, 08:26 AM
  4. Replies: 3
    Last Post: December 9th 2009, 02:57 AM
  5. Investigate the validity of Taylor's theorem for f
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 18th 2009, 11:13 PM

Search Tags


/mathhelpforum @mathhelpforum