Link to all sorts of Mathematics on the Internet

     Here are all kinds of math links to games and stories and puzzles and biographies and jokes and magic and ideas and much more.
The web is full of mathematics.
Here you'll find links to
many great math sites.

Dear Visitor,
     The Internet is full of mathematical information, fun, magic, jokes, puzzles, data, games, biographies, and inspiration. Many organizations and many ordinary people (like me) who love the subject spend time trying to make math fun for kids, teachers, and adults who either love math or have math phobias.
     Some sites interact with you. That is, they ask you to do something, and then do something in return. For example, they may let you play a game where you move a player and then the Web page moves a player in response.
     We've spent some time wandering around the Web, and have collected a few sites we think you will like.
     If you'd like to comment on any of these links, or if you can suggest other links which particularly interest you, I'd be delighted to hear from you.
Sincerely,
P.S. Clicking on any of these links will open a new browser window for you. Just close the new window by clicking the X in the upper right corner, when you've finished reading about the link.

The site Cut-the Knot is the best math site I've found, by far. It has won a great many awards. It is organized by Alexander Bogomolny, a fascinating young fellow born in Russia, who has taught math at the University level here in the states, but for the past few years has been collecting nifty samples of great math. His site has all sorts of fascinating things: games & puzzles (for example, try out the "Changing Colors" puzzle); arithmetic & algebra (try "formula for primes"); Analog Gadgets (you draw a circle in an unusual way with your mouse). He gives 27 different proofs of the Pythagorean Theorem, and his "Eye Opener Series" shows you a strange paradox. "Do you know that" gives many interesting, sometimes paradoxical math facts. He lists and describes a large number of books, and points to other good Web sites. Some of his material will be a beyond the reach of youngsters, but there's plenty that'll fascinate. If you wander off to his site and never come back here, I'll be disappointed but not surprised...
     Bogomolny offers a CD-ROM containing his entire Web page. Much of the material is a bit difficult for youngsters, but by clicking here, you'll find a list of sections that kids aged 10-14 might enjoy and easily understand. To order the CD itself, just go to Bogomolny's site, www.cut-the-knot.org and click the words "CD-ROM" at the top of the page.

On the "Not Math" page I mentioned that, in my view, history should be taught as a series of biographies...of stories about individual people who lived at various times in the past. If you look into The MacTutor History of Math, you'll find biographies of famous mathematicians, including one section devoted to ladies who made their names in this field. The site also contains a list (complete with equations and plots) of famous math curves, and sections on perfect numbers, trisecting (that is, dividing into three equal parts) an angle, and squaring a circle (that is, finding a square that has the same area as a given circle).

Kids, teachers and parents interested in math will find The Math Forum a marvelous online community of folks devoted to math and math education. It includes "Ask Dr. Math", where you can ask questions about numbers or graphs or pi or whatever you like; a math library containing complete articles on all sorts of stuff (look at its table of contents to get an idea of what's there); and a place for teachers to talk to one another, and where you can look at teaching ideas submitted by other teachers. The Forum's newspaper each week takes a subject (e.g. Helping your Child learn math) and lists several Web sites which cover that topic.

A few hundred years ago many mathematical discoveries were made by people we would now call amateurs. That is, by men and women whose primary job had nothing at all to do with math, but who found it fascinating. Nowadays most math progress is made by people who work full-time either teaching or doing research in mathematics. However, today many amateurs are interested in what's called "Recreational Mathematics". These are interesting oddities -- for example, the question as to which prime numbers read the same backwards as forwards (101 and 727 are examples).
     There is a very cool site devoted to recreations. Look in at Ivar Peterson's Mathland and you'll find a list of 100 or more recreational topics, including the one on reversible prime numbers, and others on: a Mobius strip in a park, to be climbed on; the best strategy for the game Minesweeper; and the best way to tie your shoes.

The "Game of Life" isn't really a game. It's a very large checkerboard on which you place as many players as you like. And it's a set of rules which tell you how the players change from one "day" to the next. (It is one of the Games in Gnarly Math, which gives the rules, shows how some sample starting patterns work, and lets you invent your own patterns.) There are many Web pages devoted to the game, and you can find them by searching for "the game of life" (in quotation marks) on any of the search engines.
     One excellent source is this wonderful Life Page. It shows you the rules, tells something of the history of the game, and lets you play in on-line.

If you enjoy working Puzzles, look here. This site contains many puzzles of all kinds, together with links to other puzzles and mathematical recreation pages. The puzzles are marvelous, though many are a bit hard to understand -- often the author starts talking about a group of puzzles without explaining what the puzzle is. Some puzzles are related to things in Gnarly Math--for example, "Dissecting convex figures" is related to Gnarly's tiling game. Many of the puzzles aren't mathematical at all-- for example, "Wordplay" asks you to rearrange letters in words to make other words. But they'll all help you think and reason.

Another puzzle site specializes in Magic squares and stars. A magic square is a square filled with whole numbers, arranged so that the sum of any row, column, or diagonal is a constant. Magic stars are star-shaped figures with the same feature. Here you'll find examples, rules, links to other magic-square sites, and references to the history of magic squares. The site author is not a mathematician, but his enthusiasm for his subject is catching.

If you'd like to tackle some really difficult puzzles, have a look at Nick's Mathematical Puzzles. You'll find tricky puzzles on algebra, geometry, trig, probability, numbers, and even some calculus. But you'll be challenged!

Are you a new teacher, or a parent who's teaching? You'll find a lot of useful help in this site, including lesson planning, instructions on creating a web page for your class, and many teaching resources, organized by grade.

If you like movies, visit this site. It lists about 30 movies all connected somehow with math. It includes one in which Walter Matthau plays Albert Einstein, and another in which Jon Reeves plays the part of the famous mathematician Richard Feynman. Some of the movies I happen to have seen, and liked. But most of them were new to me, and sent me to my local Video Rental Palace.

Although I'm an American, in the early '50s I spent 3 years at Cambridge University, in England. I've discovered they publish, on the Web, three interesting sites. All are part of the "Millennium Mathematics Project", which aims to "help people of all ages share in the excitement of mathematics". The sites contain problems and puzzles (usually with answers), along with articles -- which often describe games. Some puzzles are contributed by young people, so you kids hurry over and give it a try! The sites are nrich, and Plus, an online magazine. You'll find back issues there as well as the current ones.

If you or your child are particularly worried about Algebra, and find it difficult to comprehend, I can wholeheartedly recommend Josh Rappaport's Web site www.singingturtle.com. Josh, who is an award-winning teacher, publishes a free monthly newsletter "Turtle Talk" which is well worth subscribing to. Every month he gives good advice on teaching or learning math, along with a Problem of the Month (and an answer to the previous month's Problem). Turtle Talk has contained tricks to simplify calculations, a "Painless Introduction to Factoring Trinomials", and a list of good math books.

Here's a site containing several thousand word problems, aimed at all grades from 1 to 8. They are presented in a format that can be printed out, so that the student can work on them on his own, away from the computer. Many problems for young children are based on familiar stories, such as nursery rhymes. There are easy problems and difficult problems at each grade level, so a student can start with the simple ones and move up as he improves. The only trouble is, there seem to be no answers posted. So the student has no way of getting help if he can't solve a problem.

The site Cool Math is well named. Here you'll find a few math concepts very clearly and briefly explained. I haven't visited the site often, but I imagine the concepts described change from time to time.

At the Los Alamos National Labs Web site you'll find a very well-thought-out series of what I'd call 'investigations' into seven easy-to-understand but challenging math topics. One topic asks you to color several very strange maps, using as few colors as possible -- and most of these maps were submitted by kids. Another topic describes the strange hotel which never fills up. A third challenges you to put ice-cream stands in a city so that no one must walk too far for a cool treat. A fourth has you trying to tell who is lying and who is a truth-teller.
     Each topic gives you background information, suggests games ('activities') based on the math, and explains what the key mathematical ideas and concepts are. Children will enjoy all the topics, and teachers may find worthwhile classroom activities here. (I should mention that Gnarly Math goes over the map coloring problem in some detail, and that its Bridges of Konigsburg is related to Los Alamos' 'Games on Graphs'.)

Here's a site with all sorts of advice and help for students and teachers of math. At www.math.com you'll find homework help, a place to practice fractions and decimals and percentages and algebra and geometry, an "Ask the Expert" section where you can get particular questions answered, a set of Calculators and other math tools including an equation plotter, and a page of games. Highly recommended.

I recently ran across the Absurd Math site, and heartily recommend it to you. It's a place to play a game called "Pre-Algebra from Another Dimension". The graphics are gaudy, the story is absurd, and to win you must carry out some simple mathematical operations. Try it! it's fun.

At Cramster you'll find an online study community aimed at providing help on math questions whether they're related to homework, exam prep, or just general learning. It shows problems and gives answers to math questions in several math textbooks. It lets you read lecture notes and take practice exams. And it permits you to ask your own math questions, or to see questions other folks have asked. You'll have to sign up, but there's no charge.

     You will find the Game of Life, Map Coloring, the Bridges of Konigsburg, the Tiling game and a whole lot more in our math CD-ROM Solid Gold Gnarly Math.
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