Exploring Flatland Name:

The movie you are about to watch came out just a year ago, but the book on which it is based is much older. Watch the movie, the actor interviews, and the discussion on the 4th dimension, and answer the following questions. When you finish the movie, you will go to the computer lab for further work in 4 dimensions. You will turn in your paper to Mr. McRae at the end of class.

Questions about the movie and the extra features:

  1. What is the Circle Axiom? (What is an axiom? Look it up later in the computer lab if you don’t know.)
  1. What did Hex’s grandmother give to her?
  1. Who revealed the third dimension to A. Square?
  1. Complete the sentence, a quote from the movie: “______, reason, and ______will help reveal the truth.”
  1. How and why did Hex’s mother die?
  1. What is a “Super Square?”
  1. What is Abbot Square’s relationship to Arthur Square?
  1. Complete the quote from Spherious to Arthur Square: “Your ______has grasped what your ______cannot ______.”
  1. What does Tom Branchoff teach?
  1. What is a hypercube?
  1. How many points are on a hypercube?

Questions from your work in the computer lab: I have compiled a list of resources to help you investigate aspects of the fourth dimension. Do not feel limited to working with the links and sites I suggest. Go to http://siggeometry.wikispaces.com/N+Dimensions.

  1. The first row has a link to a Wikipedia article on the history of Flatland.
  2. When was the book written?
  1. Who wrote the book?
  1. Did the author intend the book to be a mathematics text only?
  1. Many of the actors offered an opinion as to the moral of the story. After having watched the movie and read some background on the text, what lesson(s) do you take from the story?
  1. The second row has a link to two websites that give explanations for the word “tesseract. “ (Some of you may recall the word from reading Madeleine L’Engle’s A Wrinkle in Time. Use the websites to help you gather together a definition of the word and write your definition in the space below.
  1. The third row has a link to models of a tesseract. Choose the jpeg movies or the gif movies to watch the models rotate.
  1. The fifth row gives a method for drawing a tesseract. This YouTube video is the first of many (15) that are embedded in the space. The other videos are interesting, but this one seems to me to be the clearest. You probably don’t have time to watch the others. Use the graph paper provided to follow along and draw your own model. Don’t worry if you cannot hear the voice. You can follow his actions easily enough.
  1. The next two rows are rotating images from YouTube that I could not resist sharing.
  1. The seventh row is a link to the website of a 4D enthusiast. His website shows a mathematical method for drawing hypercubes in N Dimensions. I have downloaded the lengthy, but clear, PowerPoint file in row 8. Row 9 contains the PowerPoint file for locating snakes in N Dimensions. If you have time, you can use the handouts in this packet to number the vertices and connect them to form a 4D or a 5D hypercube. Then see if you can find the Great Snakes!

Graph Paper for Drawing a Tesseract (Row 4 from WikiSpaces)

4D Cube by the Numbers (see rows 8 and 9 in Wikispaces)

Can you find the Great Snake?

5D Cube by the Numbers (see rows 8 and 9 in Wikispces)

Can you find the Great Snake?