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Interactive Mathematics Miscellany and Puzzles
The heart of mathematics consists of concrete
Also, some pages are organized into series while others, especially the older ones, are accessible individually. Throughout the discussions at this site I refer to various titles I love and find useful enough to have them in my own library. These are collected in a table with links to the pages where they were referred to. I have established an association with amazon.com. I bought there a few books myself, and found both the service and execution excellent. Now, on the Bookstore page, the author column has links to both amazon.com where, if you so wish, you'll be able to purchase the book, and to pages where the book has been referred to.   First off, you may want to look at the page that explains to the curious the origin and nature of my logo. It's a pentagonal knot that used to tile the background of this and subsequent pages. Many visitors have complained that the background interfered with the text making reading difficult. Until a visit to a friend of mine I didn't know what they were talking about; for I never had this trouble on my computers. So I removed the Logo. But a Lemma and a Theorem and a very real proof that exploits well known properties of parallel lines are still available. There is also a page where I offer a beautiful geometric problem. I've known the Four Travelers problem for a while and challenged quite a few people to solve it. Not one was able to solve it without help. Making it available on Internet changed the situation. Ken Ross from the Columbia University submitted a novel solution and has courteously helped me with its details. One page currently presents 78 different proofs of the Pythagorean Theorem which was a great fun putting together. Another page looks into different ways a specific statement may be related to a more general one. Other pages have educational content. Some need a browser that understands JavaScript while others include Java applets:
Magic Squares and Nim may be of interest to students of Boolean Algebra and Binary System. The main device in both games as well as in 3 glass puzzle, is a regular checkbox and, who knows?, perhaps in a while the checkbox will prove to be a valuable educational tool. ;-) Cryptarithms are brain teasers obtained when digits in numerical calculations have been replaced with letters. Known for thousands of years, cryptarithms could be solved with a pencil and a piece of paper. As you may see, besides contributing to cleaner environment, doing this on-line adds a convenience of having to replace only one occurrence of a letter or a digit - the rest change automatically. Base Converter lets one convert simultaneously from representation of a number in one base system into its representation in other systems with various bases. Three glass puzzle is a checkbox implementation of an old puzzle. Pour water between glasses until you get a required amount. A second implementation (accessible through the first one) while less pretty, is more flexible. It has controls for modifying puzzle parameters. On the Math Quotations page I collected definitions of Mathematics from various sources. It's easy for you to let me know which ones you agree with. Check the corresponding boxes and submit your selections. The polling, of course, is absolutely anonymous. On the We and Education page there is another poll. What do you think of education. How you react to what you hear, see or read. Currently there are three probabilistic problems that come with simulation devices for you to experiment and gain insight into a possible solution. Monty Hall Dilemma is a controversial probabilistic problem. At times entire Mathematics Departments were split between proponents of two different solutions. Three pancakes is similar but still a very different problem. One of the Lewis Carroll's Pillow problems demonstrates how little may be needed to generate a non-trivial riddle. Attempts to represent a number with a given digit may often lead to unexpected results. For example, 33/3-3/3 is a representation of 10 with five 3s. The Funny Arithmetic page offers a tool that helps in discovering such identities. Eye Opener Series is a collection of pages that use Java applets. All of them depend on a mouseTracker.class - a piece of Java code that controls a couple of eyes. Due to some idiosyncrasy of implementation, after you run several of this applets, the browser (I used Netscape 2 and 3 for Windows 95) refuses to load this class. Must be a bug... I am sure they'll fix it in later releases. Meanwhile, the only solution I found was to exit the browser and then restart it again. Analog Gadgets Series is a collection of Java applets that emulate analog devices. Used mostly for geometric construction, these gadgets provide an opportunity to discuss various theoretical and applied aspects of Geometry. Do you know that... is a collection of diverse mathematical facts many of which I hope will be of interest to an average visitor. The Many Ways to Construct a Triangle is exactly that: a collection of dozens of ways to construct a triangle. The CTK Exchange is a forum to ask or answer math related questions. Every one is welcome with one caveat: CTK Exchange is a place to get help in your work. You should not expect the work to be done for you. Fast Reckoning page offers advice and tips on fast calculation. How to compute fast without a calculator, how to detect a possible error, how to impress your peers with your ability. Mathematics as a language page offers for comparison excerpts from famous mathematical texts and their modern equivalents. One can't help wondering how, lacking the mathematical language, ancient mathematicians have been able to prove something which remains appreciated even today. Proofs in Mathematics is a collection of proofs selected either for their utter simplicity or unusual beauty. Manifesto is where I make a personal statement as to the purpose of this site. From there I plan to branch into educational and instructional math related topics. A monthly column for MAA Online where I try to show how Java applets may be used to help students make their own albeit small math discoveries. To me Internet is one of life's wonders. I am convinced that this new media will have an enormous impact on the society as a whole and on individual lives. It definitely became quite an important part of mine. No, I do not spend hours at a time surfing the Web. Well, except, perhaps, sometimes ;-) But my appreciation of the Web, of ease with which it connects people with people and people with sources of information, grows every time I go on-line. I discovered sites I visit often and regularly. Be my guest and enjoy various ways in which news are presented nowadays. Recently I discovered the source of the 4 Travelers problem. It appears in the Littlewood's Miscellany, B. Bollobas (ed), Cambridge University Press, 1990. Littlewood's Miscellany from Cambridge University Press, 1990. The book appeared first as A Mathematician's Miscellany in 1953 and was reprinted several times since but was out of print somewhere between 1968 and 1988. This hiatus of 20 years explains the trouble I had in locating the source.
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