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Discussion: All Tools in Algebra on Computer
Topic: Probability & Simultaneous Equations Java Applets


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Subject:   RE: Probability & Simultaneous Equations Java Applets
Author: Si
Date: Apr 28 2006

> especially when they get "unstubbed."
> Vic


There are two new applets, which have been unstubbed from the same link (see end
of message).

The first one is for 'Vectors'. This applet does vector operations as
subtractions, additions, multiplying by a number, bearings and magnitudes, area
subtended by two vectors originated from the same point, vector directions,
resultant vector from addition and subtraction of different vectors eg:  R = 3*a
- 2*b + c . Student can visualize vector operations on graph.

The second applet is for Transformation. The available transformations are:

1) Reflection:
2) Rotation:
3) Translation:
4) Enlargement:
5) Combination : Upto to a maximum of three combinations (minimum of two) from
transformation in  1) to 4) listed above for any order chosen by the user, eg:
Translation -> Reflection -> Enlargement or Rotation -> Enlargement ->
Rotation, etc,...

The key to this applet is to:
1) Select the object type to transform from a drop down box, that is, a Single
Point, Line Segment or Polygons (3, 4, ..., 7). It is defaulted to Polygon (3
points). After this, then click the 'Calculate' button, where the mouse cursor
will change into 'cross-hair' when it moves within the plotting area. Say you
select Polygon (4 points) from the combo box and then click the 'Calculate'
button. When the cursor changes into cross hair over the plotting area, you must
click 4 different points as the vertices of the object that is being
transformed. After the completion of   clicking the 4 points on the graph, the
cursor will change back to northwestern arrow and you will see the object and
the image being drawn on the graph. The points that you click on the graph will
only snap to the nearest integer point, that is it snaps to grid points.  Scroll
around if you can't see both the object and the image. There are two tables on
the left side, which shows the coordinate points of the object and the image.
Select any coordinate pair using the mouse either from the object or image table
where this will draw a link line, which shows how the object has been
transformed into the image.

The last one is the 'Combination' where the user can select a 'Transformations'
from the left list using the >> button which add that transformation to the list
on the right under 'Combinations'. You must add at least 2 different or the same
'Transformation'. There are a maximum of only 3 type of transformation that can
be used at one transformation operation. Every time you add a transformation to
the list on the right, there is a tab added to the side of the permanent tab
called 'Resultant', where the parameters for each added transformation can be
set, prior to pressing the 'Calculate' button. The 'Resultant' tab shows the
object coordinates and the final image coordinates. It does not show the
intermediate coordinates, however if you select one of the intermediate
transformation tabs and click on the object or image table data, then all the
intermediate image are shown on the graph of how it maps from the original
object to the final image. The intermediate transformations are only short
handed such as 'Tr', 'Re', ‘En’, which stands for a combination of Translation
-> Reflection -> Enlargement.

If confuse about anything, just click the 'Calculate' or click 'Clear' prior to
‘Calculate’, because there are pop-up dialog messages which help in guiding
the user of what steps that is required to do.

I am currently writing some notes for the applets that are already available to
be put up soon.


http://geocities.com/mathsforhighschool/


Cheers,
Sione.

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