Fibonacci Numbers

The Fibonacci Association is the professional organization devoted to anything and everything relating to the Fibonacci sequence. They even have their own journal, the Fibonacci Quarterly (which you can order articles from via OhioLink) that consists entirely of new discoveries about the Fibonacci sequence and the mathematics relating to it.

The biography of Leonardo Pisano Fibonacci from the MacTutor History of Mathematics website.

Prime Numbers

The Prime Pages has information on the number of primes, the distribution of primes, lists of primes, and the current largest known prime, which was just discovered in November, and has 4,053,946 digits. This prime was discovered by the Great Internet Mersenne Prime Search, which has discovered the last 5 largest prime numbers. You can become a part of the search by downloading free software from their website, and possibly win some money!

The biography of Euclid of Alexandria from the MacTutor History of Mathematics website.

The biography of Eratosthenes of Cyrene from the MacTutor History of Mathematics website.

The British publishing company Faber and Faber is offering a million dollar prize for a proof of the Goldbach conjecture. You must submit the proof before March 15. Terms and conditions are here. The conjecture has already been verified for all even numbers up through 4x10^14. Better get cracking!

Here is a webpage listing a number of factorization algorithms. For the ifactor command, Maple 7 apparently uses the Continued Fraction Factorization Algorithm developed by Morrison and Brillhart as its default algorithm, but it allows you to choose a number of additional factorization algorithms, including the Pollard Rho Method, and the Lenstra Elliptic Curve Method.

Here is a webpage about the so-called "illegal prime number" written by the guy who discovered it. This is one of the "executable primes" which, when written properly, are actually computer programs. The smallest of these is 9923.

RSA

RSA Security, the makers of RSA-based encryption and decryption software.

The Pythagorean Theorem

This webpage from the Cut The Knot math pages has 38 proofs of the Pythagorean Theorem. Over 300 are known.

The biography Pythagoras of Samos from the MacTutor History of Mathematics website.

Wallpaper Patterns

There are several good webpages exploring wallpaper patterns. A collection of links to some of these sites is here. Two that list the 17 wallpaper groups are here and here. Two excellent java applets here and here allow you to draw wallpaper patterns in each of the 17 groups. Note that there are two different notations for the 17 wallpaper groups, and some of these pages use an alternate notation than the one in your handout.

Geometry on a Sphere

This webpage has an excellent windows application for plotting and measuring flight paths on the globe. When specifying a new flight, choose the option "geodesic (great circle)" to find the shortest distance on the globe between two cities. If you select the option "mouse flights show loxodromes" and select the departure and destination points manually, the program shows both the great circle and the latitude distance between the two points. If you select the option "flight data" from the view menu, the program tells you flight distances and angles for both the great circle and latitude flight paths. This program has many other cool features. Experiment with it!
When downloading this software, you might first need to download WinZip to extract the file. Note: I do not know the writer of this software, and I cannot personally vouch for its lack of viruses. I have not encountered any problems with it, but use it at your own risk.

The biography of Johann Carl Friedrich Gauss from the MacTutor History of Mathematics website.

Erdös and Erdös Numbers

Here is the webpage for The Man Who Loved Only Numbers. For everything you ever wanted to know about Erdös numbers, check out this page. For instance, did you know that in 1987 Erdös co-authored papers with 34 people for the first time?

The Möbius Band and The Klein Bottle

This site has cool games that you can play on torus and klein bottle surfaces.

This site will sell you a Klein bottle. They're expensive, but great fun at parties.

Graph Theory

Here is a picture of a torus with seven countries drawn on it, each sharing a border with every other country.