MCS-115: The Nature of Mathematics (Fall 2011)
Useful Links

• General links

  • Textbook's webpage (requires registration)

  • What is mathematics? (an article by R. Lewis, Fordham)

• Chapter 1 stories

  • Math in the Movies (A problem similar to Story 3 is featured in a popular movie. Which one?)

  • Story 7

    • Stick or Switch simulation (java applet)

    • Another simulation

    • Another simulation which makes it easy to do 200 trials

    • More Monty

  • Why mathematicians care about hat color (this is related to the "dot problem" in Story 9)

• Pigeon Hole Principle (2.1)

  • World Population Clock

• Fibonacci Numbers (2.2)

  • Fibonacci numbers and the golden section home page

    • Fibonacci numbers and nature

    • Golden Ratio in nature

    • Who was Fibonacci

  • Fibonacci bio at St. Andrew's history of math archive

  • Fibonacci Nim (java applet)

• Clock Arithmetic and Check Digits (2.4)

  • How UPC bar codes work.

  • Check Digit Calculator

  • Practice Clock Arithmetic (with answers) (More)

  • Credit Card Validation

  • Verify check digits of UPC and ISBN codes (select Applet 10 in Chapter 8)

• Infinity (3.2, 3.3)

  • Biography of Cantor

  • Infinity at the History of Math Archive

  • Story of the Hotel Ad Infinitum

  • More about Infinity

• Pythagorean Theorem (4.1)

  • About Pythagoras

  • Pythagorean theorem and baseball

  • Pythagorean theorem in a court case (pdf)
    Case upheld by State of NY Court of Appeals

  • Proof in book (animated)

  • Another proof

    • animated applet

    • applet

    • applet

  • Euclid's proof of the Pythagorean Theorem (java applet)

  • Thirty-nine proofs of the Pythagorean Theorem

  • More proofs of the Pythagorean Theorem

• Golden Rectangles (4.3)

  • Golden ratio in art and architecture

  • The golden ratio everywhere (EKGs, teeth, nature, art, architecture, handwriting ?)

  • Controversy surrounding the golden ratio

  • Misconceptions About The Golden Ratio (George Markovsky) (pdf)

  • Review of psychological research

  • 5000 Digits of the Golden Ratio

• Platonic Solids (4.5)

  • Platonic Solids (java applets)

  • Platonic Solids (why are there only 5)

  • Another Platonic Solids (why are there only 5)

  • About Plato

  • Make your own dodecahedron desk calendar

  • George Hart's Site, containing lots of pictures, history, activities, and links related to Polyhedra in general.

• Rubber Sheet Geometry (5.1)

  • Turn an inner tube inside out (Topological Dressmaker by Ian Stewart)

  • Perplexing Pencil Puzzle

  • Sculpture inspired by topologically interesting surfaces

    • Helaman Ferguson

    • Carlo Séquin's links to similar artists

• Möbius band and Klein bottle (5.2)

  • Möbius band

    • Möbius bands and recycling

    • Lego mobius bands and Klein bottles

    • Biography of Möbius

  • Klein bottles

    • Klein bottle you can rotate (Mathworld)

    • Pictures of Klein bottle

    • Klein bottle image (John Sullivan)

    • Another good picture of a Klein bottle

    • Movies of Klein bottle (various formats)

    • Large Klein bottle(from movie)

    • Klein bottle with grid

    • Klein bottle in 4D space (Banchoff)

    • Klein bottle products

    • Torus and Klein Bottle Games

• John Conway's Game of Life (6.2)

  • Game of Life at www.math.com

  • Article in Scientific American by Martin Gardner

  • Alan Hensel's fast, powerful life applet with many complex starting patterns

  • Alan Hensel's life applet can also be found here

• Fractals and Chaos Game (6.3)

  • Fractals in the arts

  • Fractal antennas (fractal antenna company)

  • Chaos Game (Target Practice)

  • Chaos Game applet

• Chance Surprises (7.1, 7.2)

  • Pennies

• Risk (8.2)

  • Population and HIV/AIDs data (CDC) (HIV InSite)