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