Dr. Sarah's 3-d into 4-d Homer Lab
WQED Videos - Life by the Numbers
We'll watch excerpts from
The Shape of the World Video and
Mapping the earth, Global Positioning System, and
understanding the shape of the universe.
From the Life by the Numbers series.
Seeing is Believing video from Life
By the Numbers Series on perspective drawings and the 4th
For each of the following links, read thru carefully, watch the movies,
read again, and drag through the movie in slow motion using your mouse:What would a 2-d creature see when the first cube passes through its
Devide Cervone's Movie Slices of a Cube Passing Thru
Flatland(the blackboard). Pretend that a 2-d creature is standing to
the right of the cube (far enough to the right that the cube never
whacks into it!) You may answer the following with a sequence of pictures
or in words:
What would a 2-d creature see when the second cube passes through its
What would a 2-d creature see when the third cube passes through its
Davide Cervone's Movies of the Formation of
the Cube and HypercubeHow is the cube formed from a square?
How is the hypercube formed from a cube?
Davide Cervone's Faces of the HypercubeHow many faces (2-d sheets) does a cube have?
How many "faces" (3-d boxes) does a hypercube have?
Movies of the Rotating Cube and Hypercube
2-d to 3-d Homer
While a 2-d Marge or a 2-d creature can't really understand the 3rd dimension, recall that when the 2-d creature sees the orange passing through its
plane, it sees a point, then a curve getting bigger and bigger and then smaller and smaller until it becomes a point again and then disappears. The 2-d
creature understands that something appears, changes and then disappears completely and in this way sees the existence of the 3rd dimension. Also,
while it doesn't feel that there is room for the z-axis, it can understand that there could be some axis perpendicular to both the x and y axis at the same
time that it just can't see. Also, the 2-d creature couldn't see an entire 3-d Homer. Instead, it could see a layer of skin, a piece of hair or slice views
of his body.
3-d to 4-d Homer
In most respects, the Simpsons already represent a 3-d world.
For example, when the Simpsons pass one another, they don't
jump over each other as 2-d creatures would have to do.
Pretend that Homer Simpson and family had been 3-d all along
and that he changed into 4-d (length, width, height and some other
physical dimension, call it w). Think about how Homer would be
different if he changed from 3-d to 4-d.
What would happen to one piece of Homer's hair (ie it looks like
a 1-d line to the naked eye)?
What would happen to one layer of Homer's skin (it looks like a 2-d piece
of paper to the naked eye)?
What would happen to one tiny birthmark (it looks like a 0-d point to
the naked eye)?
Letter from 3-d into 4-d
due Wednesday at 5pm turned in with this completed sheet:
Write a letter from Homer to his wife Marge
discussing his jump from 3-d into 4-d.
Think about how you described Homer's jump from 2-d to 3-d in your
letter, and what pieces of this letter you could change to apply to a
letter of Homer changing from 3-d into 4-d.
In your letter, use ideas
from class, movies and the answers to the questions.
Be sure to describe the change in Homer's appearance and to use the