Three Dimensions
Try This!
Now that you've built some three-dimensional models, choose one and try drawing it in different ways:
1 Project your image in two Dimensions:
Take a flashlight and shine it on your model so that it casts a shadow on the wall. Rotate the model and see how the shadow changes.
2 Drawing Three Dimensions in Two:
Draw your model on paper. What are some techniques you can use to make it look three-dimensional?
3 Changing Your Frame of Reference:
Rotate your model or shift your position so you're looking at it from another angle. Draw your model from at least two different angles.
Next, test your imagination:
4 The Incredible Shrinking You:
Imagine you were so small that you could fit inside your model. Think of ways that the model could look different, depending on your size and your location — are you inside or outside the model? Draw at least two perspectives of what the model would look like to you.
5 Mini You and Me:
Working with a partner, pretend you're both small enough to fit inside your model. Now, both of you draw what the model would look like. Did you draw the same thing?
6 Movement and Perspective:
Imagine you are inside the box and your friend is outside the box. The box starts moving, about a foot in five seconds. After each second, how would the view from inside the box look to you? How would the box look to your friend who's watching outside? What if your friend looked at the box from a different angle?

How would you draw a four-dimensional shape? First, let's think about how you draw a three-dimensional shape, like a cube. A cube is basically a two-dimensional shape, a square, that has been moved through space. Likewise, a four-dimensional shape is a three-dimensional shape that has been moved in a direction perpendicular to our space. (This is difficult to understand since we can't really show this kind of motion.) If you moved a cube with this motion, you'd get a "hypercube," or four-dimensional cube.