## Dr. Sarah's 2-d into 3-d Homer Lab for Internet Explorer

### Due THIS Friday the 1st at 5pm and counts as one lab Revisions of this lab will be part of 3-d into 4-d Homer Lab, which will be due Wed 6th and will count as two labs (you will have part of next Monday's lab to work).

Homer Changing into 3-d from 3-d Homer from Treehouse of Horror VI 3F04 (10/30/95)

Text transcript of 3-d Homer segment and Did You Notice? by James A. Cherry
Text of Pacific Data Images description of the 3-d special
Text of How did Pacific Data Images do this?
Pictures of Homer Changing into 3-d and 3-d Homer.

### Letter from 3-d Homer to 2-d Marge

In most respects, the Simpsons already represent a 3-d world. For next week, we'll look at that more in depth. But for now, assume that the Simpson's really were 2-d creatures living in an x-y plane and that Homer and Bart had made the transformation to 3-d creatures.

While a 2-d Marge can't really understand the 3rd dimension and would feel like there isn't any room for another dimension, she could see weird behavior occurring that suggests that the 3rd dimension exists (for example the "wall" that Homer disappeared into). 2-d Marge wouldn't be able to comprehend the concept of depth or an entire 3-d Homer, since only 2-d pieces would make sense to her.

After answering the questions below, write a letter from Homer Simpson to his wife Marge which discusses his and Bart's change from 2-d into 3-d. Be sure to include mathematical explanations in addition to physical descriptions. Compare and contrast Homer and Bart's 2-d and 3-d appearances. Use the links above to answer the questions below that will help you explore 2-d life. Turn in this sheet filled out and your letter and use the writing checklist.

### Questions to Answer - Work in a Group of at Least 2 People and Answer with BOTH a Sequence of Pictures and also with Words

For each of the following links, read through carefully, watch the movies, read again, and drag through the movie in slow motion using your mouse. Then answer with PICTURES AND WORDS:

Pretend that 2-d Marge is standing in the middle of the right side of the gray shaded square (far enough to the right that the cube never whacks into her!). Notice that Marge's view of something passing through near her will be very different from your view of what actually passes through her plane.

• What do we see when the first cube passes through her blackboard?

• What would she see when the first cube passes through her blackboard?

• What do we see when the second cube passes through her blackboard?

• What would she see when the second cube passes through her blackboard?

• What do we see when the first cube passes through her blackboard?

• What would she see when the third cube passes through her blackboard?

Davide Cervone's Movies of the Formation of the Cube and Hypercube Read the text to the right of the first movie. Then watch the first movie and answer the following questions:
• How is the cube formed from a square?

• If 2-d Marge was standing at the bottom of the movie (near to the controls), then what would she see as the cube was formed?

Some other questions
• How could 2-d Marge and 2-d Lisa pass each other? (Hint - think of them both on the blackboard.)

• Could Marge eat if her mouth was located in the middle of her head? Why?

• Where would 2-d Marge's eyes have to be located? Why?

• If an orange passed through the blackboard, just next to a 2-d Marge, what would she see?

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