Math 100
Elements of Modern Mathematics
Spring 2003

Class Resources

• Fractals
  • Fractal simulators from schodor.org
    • Fractal Microscope
    • Koch Snowflake
  • Chaos in the Classroom by R. Devaney
• Fourth Dimension and Flatland
  • Questions about the Fourth Dimension asked by the class before we studied it. Take a look, how many can you answer now?
  • Flatland reading questions
  • Full text versions of Flatland by E. A. Abbot are available on line, but buy the book for $1.
    • a version that is essentially a photograph of the book
    • an html version, each section on a different web page
    • another html version
  • Tom Banchoff (Brown University) is an expert on both 4-dimensional graphics and the book Flatland. Here are some things he has put together about it
    • Math Spans all Dimension is an interactive poster with links to many other things, including
      • a Flatland web site
      • Math Shapes: Rotating 2-space, 3-space, or 4-space
    • He wrote an article about the social satire in Flatland.
    • And he gave a a series of guest lectures on Flatland Dartmouth.
  • An article Holly Durden (student in Spring 2001) found about the fourth dimension in art and literature.
  • Platonic Solids in 4D (polytopes)
    • Some info on Platonic solids in 4D (has stuff on lower and higher dimensions, too) with more links
    • Michael Gibbs has written a 4D polytope viewer. This is a Java applet to view and rotate 4D objects. You can even view them with your 3D glasses! -- Use "cross-eyed" and "red/blue" settings if blue is the left eyepiece.)
  • Some Art
    Crucifixion, Corpus Hypercubicus by Dali
  • More Animations
    • Stereoscopic Animated Hypercube
    • Watch higher dimensional cubes pass through lower dimensional planes
    • A 4-d maze game that you can install on your computer (and a 3-d analog). This tries to represent what a 4-d creature would actually see when traveling through a 4-d maze. (Hint: 4-d creatures have 3-d retinas, yikes!)
• Readings by Renyi, and Davis and Hersh
  • some reading questions
• Rationals and Irrationals
  • A Long Division Script I wrote. (Let me know if you discover bugs.)
  • Another Long Division Script
• Test 1 (Monday, Feb. 26)
  • Test 1 Study Sheet
• Solutions to Cannibals and Missionaries Problem (discussed at the end of class)
• The Proof (Nova episode on Fermat's Last Theorem)
  • Star Trek and Fermat's Last Theorem
  • Discussion Questions
• Pythagorean Theorem (March 5)
  • Handout from class [pdf]
• Secret Codes (Feb. 23)
  • Secret Codes Handout
  • Secret Codes Solutions
• Prime Numbers (Feb. 17 and 19)
  • Sieve of Eratosthenes Handout
  • Lockers Problem Handout
  • Print Prime Numbers. This page uses a sieve to find all prime numbers in a given range.
  • Lists of Primes. Another page that will make a list of prime numbers for you. (Presumably a computer is using some sort of sieve to find them.) This one has a smaller size it can handle than the one above has.
  • The Prime Pages. Lots of stuff about primes, more lists.
  • The Prime Machine.
• Fibonacci Numbers (Feb. 14):
  • Fibonacci Numbers and the Golden Mean Home Page
    • Fibonacci Numbers in Nature
    • Golden Mean in Nature
    • Quick Time Movie exploring seed heads
  • Another page with information about spirals in plants

• The 3n+1 Problem (PS 5):
  • Links for the 3n+1 Problem
  • A Worksheet to introduce you to the problem
  • Generate 3n+1 sequences on the web (in several bases)
  • On the 3x+1 Problem by Eric Rosendaal

• The Locker Problem (Feb. 9): [pdf]

This page maintained by:
Randall Pruim
Department of Mathematics and Statistics
Calvin College
rpruim@calvin.edu