4D vs 3D: A fourth dimensional person can look at something 3-D and see all of the parts of it, even the inside. From the fourth dimension you could see inside someone's body, or backpack or inside a closed box without opening it. A fourth dimensional person could also move things in a direction that goes out of our 3-D univers, so they could make part of a string seem to disappear without breaking it.

I could ask a very specific question about something like this:

1. How would your backpack look different to a 4-D person?

2. Could a 4D person take a memory chip out of the computer in our classroom without opening the case? (explain)

or I could ask a very general question:

3. Explain something that would look different to a 4D person, and how it would look.

3D vs 2D: A 3-D person can see the inside of a 2D object. If there's a shape like a square, a 2D person could see the edges of the square, but not the inside (the face). A 3D person can also put things into or take things out of a 2D cage or box without opening it

Some questions I could ask are:

4. p. 322 # 9 is a pretty good example. (the gold bars problem at the end of the 4D geometry section)

5. Draw a 2D box the way it would look to a 3D person (something like the box or toy box in the Flatland video)

6. Which of these two pictures would make the better 2-D person? Why?

7. If a 3D person took something out of a 2D universe (like flatland) what would that look like to a 2D person who was watching it?

1D: a 1D universe is really boring because you can only go forwards and backwards. You can only see things right in front or right behind you. If you were a 1D person there would probably be a lot of your universe you couldn't see or get to.

Some questions I could ask are:

8. If you were a 1D person, how many other 1D people could you see directly?

9. describe what a 1D universe is like

Here are answers to the more specific questions