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    Re: The "golden rule of three" - what's that?
    From: Frank Reed
    Date: 2018 Feb 13, 09:53 -0800

    As Don Seltzer, Brad Morris, and Bill Lionheart have already discussed, this is a rote method of solving a basic algebra problem for people who have not studied basic algebra. You might think that such techniques would now be entirely obsolete. We're nearly there, but not quite.

    For about two generations in the US, very nearly every student, even those tracked (too early!) as "not college bound" have been taught basic algebra, but for those a little older and for that small fraction who have not learned basic algebra, some rote tricks are still taught for practical application. For example, students in the "technical trades" working to become electricians still usually learn the V=I×R "Ohm's Law" pie chart. For anyone with rudimentary algebra, it's trivial to see that if you need "I" from this relationship, you get it from V/R (or to use the grade school symbology V÷R). But without algebra, a graphic pie chart serves as a mnemonic. You can see a typical example of that here. The "rule of three" was like this.

    In navigation, it's still quite common to see rules expressed in terms of "names" for angles (names being, e.g. "N" or "S") even though these are pre-algebra tricks for handling positive and negative numbers. An excellent example here is the equation for latitude at noon: Lat = z.d. + Dec (latitude = zenith distance + declination). This is the only equation ever required (for all meridian sights "above" the pole). The equation stays the same, and you handle the various "cases" by knowing that Lat, z.d., and Dec can be either position or negative (obvious that Dec and Lat are positive when "North" and easy to remember that z.d. is positive "when your shadow points north"). Yet in a great many navigation textbooks, sights for latitude by Noon Sun are still written up with rules about "same name" and "contrary name" for the arguments. The result is different rules --different equations-- for the various cases. Even when teaching 19th century navigation methodologies (Spring classes at Mystic Seaport starting soon!), this is one exception that I happily make for the modern world. We use positive and negative signs to avoid rote memorization of the various cases.

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

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