Dr. Sarah's 2-d into 3-d Homer Lab for INTERNET EXPLORER - DUE Thur 19th - ONE PER PERSON

Homer Changing Dimensions from Treehouse of Horror VI 3F04 (10/30/95)

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. Note that 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.
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 each question with BOTH PICTURES AND WORDS:

Davide Cervone's Movie Slices of a Cube Passing Through Flatland (the blackboard) 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 since she will not be able to see outside of her plane, and she will only be able to see a part of her plane (think about standing outside a building - you can't see all 4 sides at once).

• What do we see in Marge's plane when the first cube passes through her blackboard?

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

• What do we see in Marge's plane when the second cube passes through her blackboard?

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

• What do we see in Marge's plane when the third 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?

• How could a square be formed from a line in a corresponding manner?

• 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? (I find it best to answer this by repeating the shadow part of the movie.)

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

• Why couldn't Marge eat if her mouth was located in the middle of her head?

• Where would 2-d Marge's eyes have to be located for her to see things in her plane of existence? Why?

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

Letter from 3-d Homer to 2-d Marge

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.

In most respects, the Simpsons already represent a 3-d world, while an amoeba or some of the features of a Southpark cartoon seem to more accurately represent a 2-d world. For the next lab, we'll look at the Simpsons as 3-d creatures more in depth. But for now, assume that the Simpson's really were 2-d creatures living in an x-y plane of some blackboard, as Dr. Frink suggests, and that Homer and Bart had made the transformation to 3-d creatures.

Write a letter from 3-d Homer Simpson to his 2-d wife Marge which discusses his and Bart's change from 2-d into 3-d. 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.

• Be sure to include mathematical explanations (copy and paste Professor Frink's explanation of the third dimension from the above text transcript and then reiterate this in your own words).
• Be sure to compare and contrast Homer and Bart's 2-d and 3-d appearances and explain these in terms that 2-d Marge could understand (see the above Text of How did Pacific Data Images do this? link) Some things to focus on - explain what happens to their body and relate it to Professor Frink's explanation, explain what happens to their hair, and think about what happens to shadows.
• Turn in this sheet filled out and your letter and use the writing checklist.
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