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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: That darned old cocked hat
From: Hewitt Schlereth
Date: 2010 Dec 10, 18:03 -0400
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 > > > > > >