We
live in a 3Dimensional world. All objects have mass and take
up space. When we think of the space objects take up, we usually
think in terms of the objects length, width and height.
This introductory tutorial aims to demonstrate how computers
can be used to bridge the gap between the 2Dimensional textbook
world, most of us are accustomed to, and the 3Dimensional
world we live in. It will also demonstrate some of the functions
of the Mage Software Program. Many software packages now used
in schools do not allow the user to see objects as they really
are in 3Dimensions. The software package you are about to
use will present a more realistic view of an object; you will
be able to view an do measurements in 3D space. You will
be able to rotate images, make them larger or smaller and
make simple calculations e.g., distance and angle measurements.
And, one really nice thing about this software is that it's
in java. The original program and files are not on your computer
so you don't have to worry if you make a mistake. Simply click
the reload button on your browser and start again.
To
make the activity easier you might want to open another window
that contains just the text, or you might want to make a hardcopy
by printing the text page. The text for tutorial 1 is available
here.
If you look at the screen for Tutorial I, you will see two
points labeled points A and point B.
Points
are considered dimensionless; they simply are used to represent
positions in space. Click on point A. At the lower left
you will see the numbers 0,0,0 and another 0. The first
three zeros represent the x,y,z coordinates of point A.
In class you are familiar with using x,y coordinates. But
since we are now dealing in 3Dimensions we must also have
a 3rd axis. We will discuss this further in a future tutorial.
The last (or fourth) zero represents the distance between
two consecutively clicked points. Since you have not yet
clicked a second point it reads 0. Now click on point B
and see how the numbers change. The numbers now read 4,0,0
and then 4. This means point B is 4 units to the right along
the xaxis. What do you think the fourth number represents?
It represents the distance between any two consecutively
clicked points. We
will explore this further toward the end of the lesson.
Click
on the 1Dimension box at the right side of the screen.
A line segment will appear joining point A to point B. A
line segment represents an example of a 1Dimensional figure.
A true line segment has length but has no width or height.
How
many units in length is line segment AB? ______________
Click
on the 2Dimensions box. A square should become visible.
The square can be rotated in a clockwise motion by holding
down the left cursor button on your mouse and slowly moving
the mouse or mouse ball. As you move the square notice that
the square is a 2Dimensional object, it has no thickness.
If you wish to return the square to its original position
go to the VIEWS pulldown and click on View 1. Try it! If
you ever loose view of an object you can always return to
the original view by doing this or simply reloading the
image. You can change the size of the square by using the
zoom buttons on the right side (to the right of the MAGE
graphics box).
Go
to the tools pulldown and select pick center.
Click on point B and rotate the object?
Record
what has now changed _________________________________________________________
Repeat this for point A.
Click
off all objects on the screen by removing the X's on the
boxes to the right of the MAGE graphics box. Go to View
2 under Views. The screen should still be blank. Click on
3Dimensions. A cube should appear. Try rotating the cube
as you did the square.
Return
to View 1.
Explain
what happened to the cube? ______________________________________________________________
Go to View 3 and experiment with the zclip button. Move
the zclip button all the way to the right (800). Then slowly
move it all the way to the left. Explain what you think
is the purpose of the zclip tool? Why zclip and not x
or yclip?
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Now
we will take a look at a some additional features of Mage.
Click
off everything so the screen is black. Set the view to View
2, and click on the points box and 3Dimensions. A grid
of points in 3D space will appear within the cube. Click
on any point.
Go
to the tools pulldown and click on markers.
Click on some points and see what effect it has. We will
explore the the measures pulldown in a later tutorial. To
remove the
the markers
use pulldown punch. Just be careful with
punch because it will punch out anything you click on.
Undo brings it back!
Using
the cube and points experiment again with the Pulldown
pickcenter. This is important because it gives
you the point the object can be rotated about. This will
give a different perspective for each object on the screen.
Try it! Click on different vertices of the cube and see
what happens when you rotate it.
Try
now Pulldown Draw line. Click on any
two points. A line will be drawn between any two points.At
the lower left the fourth number represents the distance
between the two points. You can continue this to form a
triangle in space. After you have drawn the object you are
interested in return the pulldown to Tools to
prevent any more lines from being drawn.
Challenge
Question:
Draw
a right isosceles triangle using vertex points on the cube
with sides of 4 units. Measure the length of the hypotenuse
of the triangle (longest side). Can you check your results
using the Pythagorean Theorem?
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