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    HP's presentation on finding the symmedian point
    From: Frank Reed
    Date: 2010 Dec 18, 22:39 -0800

    Herbert Prinz, you wrote:
    "In some of the recent posts I have come across a strange notion that "eyeballing" is a method in its own right to determine the position of the MPP, quasi an alternative to various constructive methods. How can this be? How can one find a point by "eyeballing", when one does not know what to look for in the first place?"

    LOL. Very true. This 'eyeballing' is the result of what the computer scientists would call "neural network" training. If one is shown a sufficient number of cases with enough variety, then the student (or computer algorithm) can do a good job guessing the correct location without performing a detailed analysis.

    And you wrote:
    "Experience helps. "Eyeballing" is a way of implementing a given method, not an alternative to it."

    Yes, that's it exactly. The other constructions which claim to find the MPP within the cocked hat are only useful if the students really must be hand-fed a really easy method for getting close to the right spot. But no one should claim that those other points are "correct" in any sense. They're just quick "tricks" for getting close. They have become part of navigators' lore as the years have passed. On the other hand, how far off would they be?

    You mentioned the photos from your presentation in Mystic in June of 2008. Here are direct links to the two images of you and your triangles (photos thanks to Stan Klein):
    http://www.fer3.com/mystic2008/P1000529.JPG
    http://www.fer3.com/mystic2008/P1000530.JPG
    The second includes the various guesses and the correct point (the dots are the guesses and the X is the correct point).

    You wrote:
    "Every triangle that I have ever seen is close to one of the following special cases: Equal sides, isosceles, rectangular, degenerate (i.e. very very acute, very very obtuse). Know where the symmedian point is in each of these trivial cases and you will never fail to make an educated guess about the MPP."

    Maybe we need some kind of online game for this. Although many people would get quite good at guessing after reading the detailed explanation and seeing a handful of cases, I am sure that there are some who would benefit from dozens of trials. Some practical navigators would get too carried away with the construction and think that they have to do that manually every time. This is the one remaining pedagogic issue here, I think. It's not necessary to do this construction in detail every time. It's important to do it a dozen times (or so) with various triangles, and then the results will seem familiar and obvious. We have to train that neural network between our ears. And when in doubt, the construction is always at the ready.

    -FER

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