## Dr. Sarah's Geometry of our Earth and Universe

### Part 1: Problems

Work with one other person - choose a question number from Dr. Sarah's "hat". Think about what the question is asking and how you would find out the answer. For now, you may use the Dr. Sarah's globe and models, but not anything else. Prepare to present your preliminary thoughts on this problem to the rest of the class.

1. How could we tell that the earth is round without using any technology (ie if we were ancient Greeks)?

2. How could we tell what shape the universe is? Explain.

3. How could we find the shortest path between two points on a donut? Why?

4. If we head 100 miles West then 100 miles North then 100 miles East and then 100 miles South would we end up back where we started? Why? What about 3000 miles in each direction?

5. Explain why mirrors reflect left-right rather than up-down.

6. If we had a right-angled triangular plot of land between approximately Umanak, Greenland, Goiania, Brazil, and Harare, Zimbabwe, measuring 300 and 400 on its short sides, then how long is the long side from Greenland to Zimbabwe? Why?

7. On the earth, can the sum of angles of a triangle ever be greater than 180 degrees? Why?

8. What would a 4-dimensional (4 space dimensions) square look like? Explain.

9. If we slice a spherical loaf of bread into equal width slices, which piece has the most crust? Why?

10. What is a good airline path from Tallahassee, Florida to Multan, Pakistan? Why?

11. How could an ant tell that it was living on a (very large) football? Explain.

12. What would a 2-d creature's life be like?

13. Are there infinitely many stars in the universe? Why?

14. Is the surface of a sphere 2-dimensional or 3-dimensional? Why?

### Part 2: 3-d Homer from Treehouse of Horror VI 3F04 (10/30/95)

Some questions to think about and answer as you watch the 3-d Homer video:
• How has Homer changed?
• How does Professor Frink describe the 3rd dimension?
• What equations appear in the 3rd dimension? Are they true or false?

### Part 3: WQED Shape of the World Video

Mapping the earth, Global Positioning System, and understanding the shape of the universe. From the Life by the Numbers series.

### Homework

For Monday after break: Continue to think about 3-d Homer. How would Homer explain his transformation to his family? What would be the differences between 2-d and 3-d life? We'll investigate your answers in lab after break in the 3-d Homer lab.

For Tuesday after break: Investigate and try to answer your problem from part 1. You may use any resources you like. Start working on this now.