Fall 2005
MATH-125 Seminar in Mathematics: Infinity, the Fourth Dimension, Primes and Chaos: Mathematical Thinking in the Real World
Web LinksCollected here are web links to pages related to topics we investigate during the semester.- A series of 15 minute segments on mathematics from BBC 4 radio, narrated by Simon Singh:
- Five Numbers (zero, pi, golden ratio, imaginary numbers, infinity), first aired Tuesdays at 9.30am from September 25 to October 23, 2001
- Another Five Numbers (four, seven, the largest prime, Kepler's conjecture, game theory), first aired Tuesday at 9.30am, from April 22, 2003 to May 20, 2003
- A Further Five Numbers (one, two, six, 6.67 x 10-11, 1729), first aired Tuesdays at 9:30 am, from August 23 to September 20, 2005
(Thanks to Chris Muether for locating these)
- The on-line encyclopedia of integer sequences - useful for identifying sequences of numbers (for example, the sequence that starts 3, 0, 2, 3, 2, 5 that appeared in the October 11, 2005 comic strip "Fox Trot"; by Bill Amend)
- 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).
- An activity on the Art Gallery Theorem (a pdf document) based on its mention in the TV show NUMB3RS on the episode aired first on October 7, 2005 (episode 204, "Obsession"), the very same day we discussed this topic in class!
- 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 on Flatland, "Flatland: A Romance of Many Dimensions" by Edwin A. Abbott; the reading on a four-dimensional house "... And He Built a Crooked House --" by Robert A. Heinlein; 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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