|Re: HP Prime Triangle solver|
Message #20 Posted by Han on 27 Nov 2013, 1:05 p.m.,
in response to message #17 by Walter B
Also I don't take info from Wikipedia as absolute truth but sometimes as counter-evidence. The "Convention for Angles" you quote from Wiki... (!) isn't universal either though reasonable to some extent (though incomplete). Did you notice, however, that throughout above posts the angle symbol '<' is missing? Thus the point A and the angle next to it carry identical names - which is also in contradiction to the convention you quote. Thus my first post above. Please let me quote Albert Einstein: "Everything should be made as simple as possible but not simpler."
Your first post was a comment about the Prime trying to accommodate illiteracy by suggesting that alpha, beta, and gamma were the standard angle names based on a wikipedia entry and that any other labels for these angles suggests (mathematical?) illiteracy. My response to that was that the choice of A, B, and C as the labels for the angles was fairly common, if not more so than the Greek notation. This most recent response is merely a technicality about whether to include the angle symbol "<" (a best approximation due to not having that symbol readily on my keyboard). This is also a likely explanation for the lack of the angle symbol within prior posts, but I think we are both speculating, no?
As for the "contradiction" -- there is no contradiction. At best, the wiki reference I mentioned is incomplete. The first bullet, if I may clarify, distinguishes cases such as a point X, being the intersection of two lines, being used as a label for an angle because there are four angles whose vertex is X. On the other hand, if X is the vertex of exactly one, unambiguous angle, then X may be used to refer to both the angle and the vertex. And when necessary, the angle symbol is used to differentiate between an angle and a vertex. The reason for the angle symbol is because of possible ambiguity (e.g. a path through points A, B, and C given by ABC vs. the angle formed by those same points: <ABC. When there is ambiguity between an angle and a point having the same labels, then the angle symbol would add clarity where it may be lacking.
Just as we do not normally use any special symbol for any measurement (length, volume, etc), we generally do not use the angle symbol when there is no possibility for confusion. This is why one rarely ever sees "sin(<x)" in any textbook. Notice that the Greek letters in the wiki entry for Solution of a Triangle do not explicitly include the angle symbol in the calculations (in fact, it is not used at all).
As for Einstein's quote -- would it not be simpler to stick with regular letters (and differentiate via upper/lower case) as opposed to having two different alphabets?