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Discussion: All Tools in Geometry on Computer
Topic: Can anyone use this? (Geometry)


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Subject:   RE: Can anyone use this? (Geometry)
Author: Mathman
Date: Feb 15 2005
On Feb 15 2005, Karore wrote:
> Seems very good, If you like to develop more tools like this to make
> Mathematics interesting please contact me at statistics@shaw.ca

How would you use it in
> > grade 7?  What are they trying to study?  Since you say they are
> > drawing the triangles, it isn't likely the simplest application,
> > similarity, so is it trigonometric solution of triangles?
> David.

Before there is any misunderstanding of intent here, I do not belittle Jeff's
contribution in any way.  Keep it up Jeff!  My query on what use it is put to is
still deserving of an answer, and I'd also be itnerested in what use you might
be thinking of.  My intent is to pass along anything I glean to my colleageus,
for whom I do a lot of hunter-gathering, even though now retired.

With regard to this particualr process, the angles are readily found from the
Law of Cosines, and as I suggested, a spreadsheet is an excellent tool for doing
that sort of calculation.  I did this quickly in Open Office's Calc spreadsheet
[open source, as in FREE], but any would do:

In A1,B1,C1 put the three side lengths, say 3, 4, 5.
In D1 put =ACOS((A1^2+B1^2-C1^2)/(2*A1*B1))*180/PI()
In E1 put =ACOS((B1^2+C1^2-A1^2)/(2*B1*C1))*180/PI()
In F1 put =ACOS((C1^2+A1^2-B1^2)/(2*C1*A1))*180/PI()

...and you are done.  Also, it is noteable that this gives the 90 accurately, as
it should, this being a right triangle.  Copy/paste from here to save typing if
you want to try it.

If you wanted to, this could be taken further by dragging the formulas down a
few cells, and filling in some more valid values for triangle sides. [An error
would show until side values were filled, or there could be an error trap.]

The question remains as to what purpose this might be put in the classroom.  The
only one I see here is possibly similar triangle relationships, and I am
wondering of that is studied now in grade 7.  I am also wondering what use you
might have in mind if you don't mind sharing.  I've done a few spreadsheets in
arithmetic an algebra, and have given them away free if the cause is just.

David.

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