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 84 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 game [JavaScript, Frames]
- The game of Nim [JavaScript, Frames]
- Cryptarithms [JavaScript, Frames]
- Base Converter [JavaScript]
- 3 glass puzzle [JavaScript]
- Math Quotations, a Web poll [JavaScript]
- We and Education, a Web poll [JavaScript]
- Probabilistic problems and simulations [JavaScript, Java]
- Interactive Mathematics Activities, a collection of JavaScript and Java pages with minimum up-front explanations
- Funny Arithmetic [JavaScript]
- Eye Opener Series [Java]
- Analog Gadgets Series [Java]
- Inventor's Paradox
- Did you know that...
- The Many Ways to Construct a Triangle
- The CTK Exchange [JavaScript]
- Fast Reckoning
- Mathematics as a language
- Proofs in Mathematics
- Manifesto
- A monthly column for MAA Online
- Sangaku: Reflections on the Phenomenon
Glossary is a listing of terms defined and named theorems proved at this site. Quite a collection!
Smart and clever as we are, there are still impossible things that we may comprehand but not accomplish
In this section of the site solutions to a variety of problems are given in an outline with missing pieces. This is a perfect way to provoke students' thinking
The biggest portion of the site is devoted to problems in geometry
Algebra and arithmetic are branches of mathematics that grow on the same stem. Both are powerful and both are fun
Mathematics is really a great fun. There is no wonder that math games and puzzles come in abundance
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. ;-)
Nim is the most fundamental, in fact a prototypical, combinatorial game, with many delightful variations.
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 JavaScript 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.
Probability is a branch of mathematics that provides tools for the study of random events
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 to illuminate math facts. A real eye opener - and in more than one sense at that
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.
Did 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.
The 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 tried to show how Java applets may be used to help students make their own albeit small math discoveries.
The site makes an extensive use of Java. There are more than 1000 interactive Java applets
Sangaku are often colorful tablets offered in shinto shrines (and sometimes in buddhist temples) in Japan and posing mathematical problems. At the site there are more than 60 illustrated examples
Quite often a more general problem may prove easier than a more specific problem
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.
