The Shape of Our Universe

Objectives

• Students will be able to distinguish between bounded and boundless spaces.
• Students will be able to distinguish between finite and infinite spaces.
• Students will apply concepts of space learned from previous activities to our three-dimensional universe.

Materials

• The Shape of Our Universe Activity Sheet
• The Shape of Space video

Activity

When students have completed the worksheet, discuss how this all applies to the three-dimensional universe we live in. Let students express their ideas of what the universe might be like. Do they think it's boundless? Is there an edge of the universe? Does space go on forever? Could you go forever in a straight line and never see the same thing twice?

Show The Shape of Space video again as a final wrap-up.

Answers

1. boundless: c (Klein bottle) and e (projective plane)
2. bounded in all directions: b (disc)
3. part bounded, part unbounded: a (annulus) and d (Möbius band)
4. finite: all of the below
5. 1. a line: infinite
   2. a line segment: finite
   3. a ray: infinite in one direction, finite in the other
   4. a circle: finite
6. 1. infinite and bounded in all directions: No.
   2. infinite and boundless in all directions: Yes. (e.g. a plane)
   3. finite and bounded in all directions: Yes. (e.g. a disc)
   4. finite and boundless in all directions: Yes. (e.g. a torus)

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