Up: The Shape of Space Curriculum Materials

Dimensions - Exploring Flatland

Students will learn several ways in which living in two dimensions is more restrictive than living in three dimensions.

Have students explore what it would mean to be a two-dimensional being instead of a three-dimensional being. Ask a volunteer to come up to the board and draw a two-dimensional animal (a flatlander). The most common mistake that people make is with the placement of the flatlander's eyes. A person's first attempt at drawing a flatlander usually has the eyes on the inside of the head:
If this happens, ask the students, "How will the flatlander see another flatlander?" Also, people usually draw the mouth on the inside of the head, too. Then how will the flatlander eat? A reasonable second attempt at a flatlander head could look something like this:

Either continue discussion as a class, or let students explore possibilities in small groups using the questions on the activity sheet provided.

At the end of the activity, look again at the flatlanders in The Shape of Space video. Ask the students some questions:

How did the makers of the video deal with the flatlander issues that the students explored today?
Where did they place the eyes?
How would it look to us 3-D people if the flatlander took a swim in the lake? Could we still see him when he went under water?
Would the flatlander get wet?
How many other things do you notice about how the flatlanders were designed?

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