Spring 2004

MT-A125 Seminar in Mathematics: Infinity, the Fourth Dimension, Primes and Chaos: Mathematical Thinking in the Real World

Web Links

Collected here are web links to pages related to topics we investigate during the semester.

Click and Clack posed a "two glasses of water" puzzle in May 2001; more puzzles from "Car Talk" in their archive (for Chapter 1).
Examples applying the pigeon-hole principle (some are to deeper mathematics), and more examples (for Section 2.1).
A wealth of information and activities about Fibonacci Numbers and the Golden Ratio (for Section 2.2)
A prime site for prime numbers (for Section 2.3)
A selection of sites about Fermat's Last Theorem as indexed at Yahoo (for Section 2.3)
Information about unsolved prime problems (for Section 2.3)
You, too, can use full-strength public key codes (for Section 2.5)
Alas, only a finite number of sites about infinity: FAQ on large numbers (at the Math Forum); a version of the Hilbert (or Cardinality) Hotel story (a page from the MegaMath project at the Los Alamos National Laboratory) (for Chapter 3).
A page on the golden section in art and building (for Section 4.3)
A page at the Geometry Junkyard about tiling - look at the picture at the bottom of the page! A page on tilings related to our pinwheel tilings (for Section 4.4)
Stretch out into the twilight zone with these sites on the fourth dimension: Links to various fourth dimension resources; the reading for Wednesday 3/17, "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott; "... And He Built a Crooked House --" by Robert A. Heinlein; the reading for Friday 3/19; short movies illustrating fourth dimension principles, used in a math course at Union College; short movies illustrating hyperspace structures, at Loughborough University in the U.K.; a student paper on the fourth dimension and art (with links to artwork, or see the Gallery page); a whimsical piece of luggage (for Section 4.7).
More twists on Möbius bands and Klein bottles: Math That Makes You Go Wow (student work for a multi-disciplinary course at Yale); an animated crab swims in the surface of a Klein bottle (see also the game site below); Klein bottle + limericks (part of a larger site on the fourth dimension);games played on the surface of a torus or a Klein bottle; buy a Klein bottle (or not?) (for Section 5.2).
To be or knot to be - an exhibit of knots (for Section 5.4).
Dead or alive? - sites catalogued at Yahoo for Conway's Game of Life - also for online java examples; one nice page is www.math.com's (for Section 6.2).
Among the chaos of fractal pages, these applets by Bob Devaney (at Boston University) are gems (for Section 6.3).

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Spring 2004MT-A125 Seminar in Mathematics: Infinity, the Fourth Dimension, Primes and Chaos: Mathematical Thinking in the Real World

Web Links

Spring 2004

MT-A125 Seminar in Mathematics: Infinity, the Fourth Dimension, Primes and Chaos: Mathematical Thinking in the Real World