| > Component vector => again I like this since it is self-describing
|
| I have no objection to that, although IMHO "projection" is
| more concise, is equally self-describing, and is already
| well-established in the math and physics literature.
And Jeffrey S. wrote in part:
|"scalar projection"
|indicates that some people think that there are at least
|two kinds of projections of a vector onto another vector.
The "fact" that not everybody uses the word projection to mean a vector
causes some problems. So I'm a bit bothered by the idea of using that
term for "component vector".
However, upon further reflection and reading I have the following
"possibly helpful suggestion".
In the introductory course one as the problem of trying to remove
ambiguity of terminology (the problem with the word "component" as has
been pointed out in recent posts) and the problem of terminology that
they already "know" which ain't "correct" or is confusing; compounded by
the more significant problem of trying to get the concepts across. One
also should pay some homage to standard terminology. This discussion is
all about trying to use terminology that aids in getting the concepts
across; without doing undo violence to standard terminology.
I think I shall do the following:
1) Start out talking about the concept of a "component vector" and
using those words, when I first introduce the idea. I think this does
have the virtue of being self-describing in the context of "what
vectors; parallel to the coordinate axes add up to the vector of
interest".
2) Then very quickly take advantage of this conversation to teach the
"proper" use of the word projection (i.e. eschew the idea of 'scalar
projection'.)
"there already exists a word in mathematics that is used for this
concept of a 'component vector', it is called a 'projection'".
The idea is that this would all be in the same class period, so that
after the concept of a component vector is made, one refers to it as a
projection from then on.
_________________________
Now what to call the "array element"?
I prefer "array element" to "matrix element"; simply because most intro
students will come to the table thinking that a matrix is either a
square array or maybe the more sophisticated will think of a rectangular
array.
I'm warming to this idea (more for lack of any other). I've never been
particularly fond of writing vectors as
(v_x,v_y,v_z)
preferring unit vectors
V = v_x e_x + v_y e_y + v_z e_z
OTOH, most of my students come to me more familiar with the 1st version
where the words "array element" are quite natural.
So I'm warming to this idea as well. I can start with the probably more
familiar (v_x,v_y,v_z) and define an "array element", should be familiar
to most of my students; then quickly segue to unit vector methods.
_______________________________________
So I have.
Component vector -> which except at the very beginning I'll call a
"projection"
Asides, I usually take the opportunity to mention as an aside the words
"direction cosines" when talking about this topic. While less true
nowadays, students often have heard these words without understanding
them.