Do you mean calculations with vectors?I think some students may be understandably inclined to post analytic/coordinate geometry questions in our Geometry sub-forum, so I would suggest adding:
to the Pre-Calculus sub-forum description for clarification.
No, I actually mean geometric questions that involve using a coordinate system for the solution. A good example is locus problems, such as:Do you mean calculations with vectors?
If so, how about Vector Calculus?
I just checked and currently our smallest category is actually Geometry (58 threads), except for Other Topics (34).No, I actually mean geometric questions that involve using a coordinate system for the solution. A good example is locus problems, such as:
Find the locus of points equidistant from the line $y=k$ and the point $(a,b)$.
While it is technically a problem in plane geometry, it involves using coordinates and the distance formula, rather than Euclidean theorems/postulates/axioms.
Ah, my bad. I didn't read carefully enough.I'm not suggesting that a new category be created, only that the description of the Pre-Calculus sub-forum be amended to include Analytic Geometry.
I would tend to want to put Vector Geometry problems (not involving the calculus) in the Pre-Calculus sub-forum as well, as we have done in the past, but this may be to a bias on my part towards U.S. mathematics education conventions.
I would be happy to see categories 1. and 2. put into the geometry subforum. There are plenty of problems in both analytic and vector geometry that can be solved either by analytic or synthetic methods, and it can often be instructive to see both methods of solution.As I see it, there are 3 categories involved here that don't really have a proper place yet:
- questions about distance to a locus or a line using coordinates (analytic geometry),
- questions about solving geometric problems using vectors (vector geometry),
- questions about a basis of vectors, orthogonality, normality, and so on (pre-linear algebra)
Mark wants to put all of them into pre-calculus, since apparently in the States they are taught in that class.
Deveno points out that "pure" geometry (axioms, congruences, and such) is hardly practiced any more, although he does not seem to show a preference where the 3 categories should go.
I would prefer to put them all into geometry since as a category that seems a better fit to me, and also because geometry is pretty small right now.
It would be nice if some others would put in a comment.
Added "Analytic or Coordinate Geometry; Basic Vector Geometry" to the Geometry description. It seems to me that more advanced vector operations, such as the cross product, belong in a more advanced forum than geometry. Pre-Calc would be fine, or even Linear Algebra. Thoughts?I would like to see the description of Geometry expanded to include coordinates and vectors, so that members can tell where to put such questions.
Nice!Added "Analytic or Coordinate Geometry; Basic Vector Geometry" to the Geometry description. It seems to me that more advanced vector operations, such as the cross product, belong in a more advanced forum than geometry. Pre-Calc would be fine, or even Linear Algebra. Thoughts?
Or they could go into Other Topics, as I think many geometry courses do not cover the cross product, but any physics course worth its salt will.Nice!
I'd say that the basic application of the cross product to find a normal vector can also go into Geometry.
Both of those are also taught in Multi-variable Calculus, so it could go into Calculus as well. If it's more theoretical, then Analysis would be better.More advanced theorems and outer product generalizations should go into Linear Algebra.
I think that curl and Stokes fit in Analysis.
Sounds good. I'm not sure any of these thoughts would need to go into the forum descriptions, though. I think these nice judgements would be better done simply by moderator.Advanced applications, such as in 3D mechanics, should fit in Advanced Applied Mathematics.