# Fourth dimension exercises

1. a. Why do Flatland houses look like pentagons, not triangles or squares?

b. Can the house look like a regular n-gon for larger values of n?

c. What would you expect a church to look like? Why?

2. How do inhabitants in Flatland move from one class to another?

3. There is a short story about a traveler who found Flatland in the basement of a Pakistani restaurant in London. In Flatland (the original) the sphere interacts with Flatland and its inhabitants by passing through Flatland.

a. What would the Flatlanders see if a person interacted in a similar way? b. The soldiers attack the visitors. What do the soldiers look like, and how would they attack this person?

4. Mr. A. Square is visited by the Sphere from Spaceland. What if the square was visited by a Cube? What would A. Square see? Explain. Think carefully about what possible intersections the cube could have with the plane.

5 a. When the Sphere removed A.Square from Flatland, what did A.Square see?

b. Suppose a 4-dimensional being removed you from this space. What would you see if you looked "down" on our 3-dimensional world?

6. How many books or movies can you think of that deal with the fourth dimension?