1-DIMENSION, 2-DIMENSIONS, 3-DIMENSIONS ...
We live in a 3-Dimensional 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 2-Dimensional textbook world, most of us are accustomed to, and the 3-Dimensional 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 3-Dimensions. 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 3-D 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.
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 3-Dimensions 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 x-axis. 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 1-Dimension 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 1-Dimensional 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 2-Dimensions 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 2-Dimensional 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).
to the tools pulldown and select pick center. Click
on point B and rotate the object?
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 3-Dimensions. 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 z-clip tool? Why z-clip and not x or y-clip?
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 3-Dimensions. A grid of points in 3-D 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.
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?