The Mac programs have, for the most part, been removed from this page for space considerations. They are all freely available if you look for them.

As time goes by, these links are mostly obsolete.
Check my Escher book instead.

Contents:

• General
  • History
  • Geometry
• Math 110 - Mostly Number Theory
  • Ancient Mathematics
  • Nim & Other Games
  • Numerology
  • Euclidean Algorithm
  • Primes
  • Cryptography
  • Fibonacci Numbers And The Golden Section
• Math 111 - Mostly Geometry
  • Ruler And Compass Constructions
  • Non-Euclidean Geometry
  • Cartography
  • Tessellations
  • Symmetry
  • Platonic Solids
  • Art And Math

There are links to specific parts of this archive scattered throughout these resources.

Geometry

• The coolest site around is the Geometry Center - but the math is advanced. Sadly, they lost their funding so nothing is new here.
• Also excellent is the Geometry Forum and if you have geometry questions you can ask Dr. Math and expect answers.
• Finally, to see some real world applications of geometry, ranging from medecine to architecture, check out the Geometry In Action page.

Ancient Mathematics

• The MacTutor Archive's history of Babylonian and Egyptian mathematics.

Nim & Other Games

Or, for a much more elegant version for the Macintosh which also includes a bunch of other Nim-like games, download the "Friends of Nim" progam by clicking here. This program is 160K.

Numerology

• More than you wanted to know about the number 17.
• More than you wanted to know about the number 42.

Euclidean Algorithm

Primes

• When numbers are placed in a spiral arrangement, the primes make unusual diagonal lines. Examine this mysterious behaviour with the interactive Spirals page.
• Check out the largest known primes page. It's also got information about primes that relates to stuff we learned in class, if you're looking for more information. For example, the Sieve of Eratosthenes, Fermat's Little Theorem, or Probabalistic primes.
• The Primes Page is chock full of good information.
• The MacTutor Archive's Historical Introduction To Primes

Cryptography

• For some somewhat technical history of some famous cryptography problems (including the Beale ciphers), check out the rec.puzzles cryptology FAQ

  Public Key

  Public key has become a heated scientific and political topic. Find out why at these other sites:
  • RSA Labs Cryptography faq (there's some fascinating facts about the "Clipper" chip here - the government has a back door to eavesdrop on encrypted information)
  • The Electronic Frontier Foundation - a non-profit organization that is heavily involved in the current legal and moral issues facing privacy on the Net.
  • The Center For Democracy and Technology - a non-profit group. They have good current news.

Fibonacci Numbers And The Golden Section

• The somewhat good Golden Mean page.
• Dail's The Sacrament of the Last Supper
• Fibonacci Gamelan Rhythms - yep. Music and mathematics. I'd love to hear a performance of this.

Ruler And Compass Constructions

• The series of pages called seeing is believing is actually part of an elementary online textbook, called Math To Build On. It will walk you through some elementary and not-so-elementary constructions. I highly recommend this, especially if you're having trouble.
• Yes, you can trisect any angle! You just can't do it with an unmarked straightedge and a compass.
• For a detailed look at why certain numbers are constructible and others aren't, and in particular why you can't square the circle, examine this article.
• Here's a brief note summarizing which regular polygons are constructible

Non-Euclidean Geometry

• Don't miss Kaleidotile - a program for the Mac that displays certain tessellations in spherical, euclidean, and hyperbolic geometry. This program will really help you visualize these geometries. And it talks,too! It's 529K, so it may take a moment to arrive on your computer. (This program was created by the Geometry Center).
• Don't miss Hyperbolic MacDraw - a 20K Mac program that lets you draw shapes in hyperbolic space. The best part is that you can then move them.. the shape and size in hyperbolic space don't change, but they appear to in the distorted map of hyperbolic space that we use. (This program was created by the Geometry Center).
  Note: This program is old. If you are using a newer "Power" Macintosh, it may tell you that you need a coprocessor. It's probably not worth the effort, if this occurs. Sorry.
• A nicely done page of hyperbolic tessellations.
• Thomas Banchoff has a page explaining how, in spherical geometry, you can construct a quadrilateral with two right angles having the same area as a given triangle.

Tessellations

• For a program for the Mac that can help you draw your own tessellations, download Kali. It's big (about 800K), so it may take a minute to download.
• The Escher Patterns page is extremely good. It's got lots of tessellation artwork. Unfortunately, it's in Japan so it's really slow.
• For good pictures of spherical, Euclidean and hyperbolic tessellations, download Kaliedotile from the non-Euclidean geometry section.
• To see Penrose tilings, try the Geometry Center's interactive Quasi-Tiler application.

Symmetry

• The definitive description of the 17 possible symmetries of wallpaper, with pictures.
• A whole course on wallpaper and frieze symmetry is online. It's called Symmetry And The Shape Of Space. There's a lot of information here, and it goes farther than we do in class.

• Occult correspondences of the Platonic solids.
• For good pictures of all the platonic solids, plus more, download Kaliedotile from the non-Euclidean geometry section.

• The Mathematica Gallery - more math than art, a collection of pictures created with Mathematica.

  Some artists that combine math and art:

• M.C. Escher
  Easily the most well known and most successful artist to build on mathematical themes. In particular, many of his works are based on tessellations.
  The best site I've come across is the World Of Escher. They have a contest for tessellations, so if you make one for this class, you might consider entering.
  
• George W. Hart (very cool)!
• Helaman Ferguson. Well known. Here's something he did with snow.
• Buckminster Fuller
• Dennis North
• Guenter Albrecht-Buehler

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