The Curvature of Space: Worksheet

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1. What possible shapes could you see as the cube passed through Flatland?

    

    

    

2. What would a 4-dimensional sphere look like if it passed it through our space?

    

3. Name three geometrical tests to see if your universe is positively curved.

    

    

4. (no answer required, but read it carefully!)
5. What do you guess is the curvature of the surface in Figure 3?

    

6. What is the curvature of the surface in Figure 3? (Show your work!)

    

    

    

7. How might you use two beams of light to figure out what the local curvature of our universe is?

    

    

   What dominates the curvature in the inner solar system? Is it flat, positive or negative? How do we know?

    

    

8. Could we use geometric tests on the whole Universe? Why or why not?