MCS-115: The Nature of Mathematics (Spring 2010)
Useful Links
MCS-115 homepage
Assignments and
class schedule
Useful Links Archive
Tentative Schedule
Homework Guidelines
Project
Karl Knight
Course description
Russ Park
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
)