f
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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