Results 1 to 3 of 3

Math Help - Help! Conditioning problem

  1. #1
    lya
    lya is offline
    Newbie
    Joined
    May 2014
    From
    Romania
    Posts
    1

    Help! Conditioning problem

    I have to solve the following problem : Area of a triangle is given by S = 1/2 ab sin(γ) (See figure).
    Discuss numeric conditioning of S. Any tips appreciated..
    Help! Conditioning problem-triangle.png
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,932
    Thanks
    782

    Re: Help! Conditioning problem

    What do you mean by conditioning? If you mean numerical conditioning, then it assumes some algorithm to approximate area. Do you have such an algorithm? Then the conditioning is just \text{alg}(a,b,\gamma)-\dfrac{1}{2}ab\sin(\gamma) (which is the error of the estimation).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,789
    Thanks
    1147

    Re: Help! Conditioning problem

    Quote Originally Posted by lya View Post
    I have to solve the following problem : Area of a triangle is given by S = 1/2 ab sin(γ) (See figure).
    Discuss numeric conditioning of S. Any tips appreciated..
    Click image for larger version. 

Name:	triangle.png 
Views:	7 
Size:	14.6 KB 
ID:	30932
    take the total derivative of S.

    this gives you the error as propagated through the area formula for the errors in your 3 parameters.

    after a bit of work you come up with

    $dS=S\sqrt{(d\gamma)^2\cot^2(\gamma)+\left(\dfrac {da}{a}\right)^2+\left(\dfrac {db}{b}\right)^2}$

    the terms with $da$ and $db$ are likely to be small unless the triangle is small with respect to your measuring capabilities. Assuming it isn't we can neglect these 2 terms. That leaves

    $\dfrac {dS} S \approx d\gamma \cot(\gamma)$

    The problem lies where $\cot(\gamma)$ gets very large, i.e. very small angles, or angles near $\pi$ radians. The limit of both of these is a line segment, not a triangle and so you can see where the problem is.

    You should replicate all this so you understand where it comes from.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conditioning
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 7th 2010, 10:01 PM
  2. conditioning problem - homework due very soon
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: March 8th 2010, 04:31 AM
  3. Conditioning on a RV
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 1st 2010, 06:05 AM
  4. Conditioning problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 23rd 2009, 03:49 PM
  5. Serious help - Conditioning problem
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 23rd 2009, 03:34 PM

Search Tags


/mathhelpforum @mathhelpforum