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    Re: Obtuse versus acute cocked hat
    From: Bill Lionheart
    Date: 2019 Mar 26, 10:32 +0000

    Slightly as an aside here are a couple of Geogebra animations people
    may like to play with
    
    In both the triangle is A,B,C and you can drag the vertices of the
    triangle around to see what happens
    
    This one plots an example of a least squares ellipse and the axes. The
    points labelled X1344 an X1345 are Kimberling triangle centres that
    lie on the major and minor axes of the ellipse. F1 and F2 are the foci
    of the ellipse
    https://www.geogebra.org/classic/jtc8czqb
    
    In this one the Orthocentre H and the Circumcentre O of the triangle
    are plotted. But if you look on the left you will see three
    interesting parameters J=|OH|/R  where R is the circumradius. Q the
    sum of squares of sines of interior angles, which was mentioned by
    Robin in a post he quoted on this thread, and the condition number of
    the system of equations for the fix which is 1 for equilateral (best
    conditioned system) , Between 1 and two 2 for acute and more than 2
    for  obtuse.  Not J goes from zero to 3.  Drag around one vertex and
    go from equilateral through right angle to acute and see how they
    change.
    
    https://www.geogebra.org/classic/ytk42cnd
    
    
    Bill
    
    On Sat, 23 Mar 2019 at 16:33, Robin Stuart  wrote:
    >
    > Bill,
    >
    >      My point (which is somewhat buried in this post) is that from a purely 
    statistical point of view the obtuse 0°, 60°, 120° triangle is equally as 
    good as the equilateral 0°, 120°, 240° one since they both constrain the 
    observer's position equally well. The equilateral triangle wins in the 
    presence of a systematic error like I.E. and any empirical bias toward 
    against obtuse triangles has that as a justification,
    >
    > Regards,
    >
    > Robin
    >
    > View and reply to this message
    

       
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