Three Dimensional Sketching

Department of Mathematics	William Paterson University of New Jersey

Jan Paxton

Wood-Ridge High School

TOPIC:

LEVEL:

Geometer's Sketchpad: Geometry: High School 9-12

GEOMETER'S SKETCHPAD PROFICIENCY:

Students should be familiar with drawing segments and points, selecting, copying, and moving groups of objects. This lesson uses, from the Transform Menu, the Mark Vector, Mark Center, Translate, and Dilate features.

CLASS TIME:

If you lead the class through the first two parts of the activity, that much will take about 40 minutes. After doing that much, most students will be able to complete the other two drawings on their own.

NOTES TO TEACHER:

After completing this lesson, the class should have a clear understanding of how perspective drawing differs from three dimensional sketching, how to do both types of drawing, and what is meant by a vanishing point. This lesson fits nicely into Chapter 1 of the UCSMP Geometry text.

Student Worksheet
THREE DIMENSIONAL SKETCHING USING THE GEOMETER'S SKETCHPAD

Sketching in three dimensions is difficult for most people. The computer can help you make nice sketches. We will be doing two types of sketches: those that "look" three dimensional and those that are drawn in perspective. We will not bother to construct any of the original shapes we use, but even nicer drawings could be made if we did.

Drawing 1: Telephone Poles going off into the distance

Step 1: Draw a telephone pole, then copy it, paste it, and move the new one over.

Step 2: On the left we will make the drawing without perspective. Make a new point behind and to the right of the bottom of the pole. Select the point at the bottom of the pole and then the new point, then, from the Transform Menu, choose Mark Vector.

On the right hand drawing we will make the drawing in perspective, so that the poles appear to be disappearing into the distance. First make a new point way back and to the right of your pole. This will be the vanishing point of the sketch. Select this point and, from the Transform Menu, choose Mark Center.

Step 3: In the drawing on the left, select the entire telephone pole. From the Transform Menu, choose Translate and then By Marked Vector. Repeat this translation until you have a nice set of poles.

Step 4: In the drawing on the right, select the entire telephone pole. From the Transform Menu, choose Dilate. When the dialog box comes up, choose Fixed Ratio and make the number for "New" 0.75 and the number for "Old" 1.00. Choose OK. Repeat the dilation the same way until you have a nice set of poles disappearing into the distance.

Drawing 2: Box

Open a new sketch. Draw a square, or something that looks like a square, copy, paste, and move it so that you have one on the right and one on the left. Construct the points behind and to the right to be used to Mark Vector on the left and as the Vanishing Point to Mark Center on the right.

Now, use the steps we used on the telephone poles to translate the square on the left and dilate the square on the right.

Connect the front vertices to the corresponding back vertices to complete your boxes. You can use the Display menu to change the segments which are "behind" to dashed segments.

More Drawings

Open a new sketch. Now that you have followed the steps through two sketches, see if you can do the drawings of the Floor Tiles and the Bird Houses. When you finish, print out your drawings and write a brief explanation of what happens to line which were parallel in the original three-dimensional object. You will need to write a different explanation for each type of drawing.