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    Re: That darned old cocked hat
    From: Hewitt Schlereth
    Date: 2010 Dec 10, 18:03 -0400

    Question: Is there any way to determine where around the cocked hat
    the fix is? I mean, are there circular bands around the cocked hat
    having greater or lesser probabilities of containing the fix, like the
    ring road around Washington DC might have McDonalds or Wendys or
    Burger Kings clustered around at different distances off the road, one
    of them being the fix?
    
    Hewitt
    
    On 12/10/10, Herbert Prinz <666@poorherbert.org> wrote:
    > On 2010-12-10 02:44, John Karl wrote:
    >>
    >> Frank & Herbert,
    >>
    >> I can see in the Villarceau article (without any knowledge of French)
    >> that he obtains the construction of the symmedian point that Prince
    >> mentions. But does he show that it minimizes the sum of the squared
    >> distances to the three sides?
    >>
    > Karl,
    >
    > As I said before:
    >
    > "When solving the minimum condition by partial differentiation,
    > Villarceau found the solution to be at the point for which the distances
    > to the sides of the triangle are as the sides of the triangle
    > themselves. (In other words x:y:z = a:b:c)"
    >
    > So, yes, he did.
    >
    > And I further said:
    >
    > "This is a defining property of the symmedian point. Lemoine showed
    > independently, but around the same time, that the symmedian point has
    > the property of minimizing the square sum of the distances."
    >
    > So, Lemoine did, too.
    >
    > Herbert Prinz
    >
    >
    >
    >
    >
    >
    
    
    
    

       
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