Interactive Mathematics Miscellany and Puzzles

The heart of mathematics consists of concrete
examples and concrete problems.
P.R.Halmos, How to Write Mathematics
AMS, 1973

There are several ways to access discussions at this site.

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 118 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:

  1. Magic Squares game [JavaScript, Frames]
  2. The game of Nim [JavaScript, Frames]
  3. Cryptarithms [JavaScript, Frames]
  4. Base Converter [JavaScript]
  5. 3 glass puzzle [JavaScript]
  6. Math Quotations, a Web poll [JavaScript]
  7. We and Education, a Web poll [JavaScript]
  8. Probabilistic problems and simulations [JavaScript, Java]
  9. Interactive Mathematics Activities, a collection of JavaScript and Java pages with minimum up-front explanations
  10. Funny Arithmetic [JavaScript]
  11. Eye Opener Series [Java]
  12. Analog Gadgets Series [Java]
  13. Inventor's Paradox
  14. Did you know that...
  15. The Many Ways to Construct a Triangle
  16. The CTK Exchange [JavaScript]
  17. Fast Reckoning
  18. Mathematics as a language
  19. Proofs in Mathematics
  20. Manifesto
  21. A monthly column for MAA Online
  22. Sangaku: Reflections on the Phenomenon

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.

Last Updated: October 16, 2017
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Copyright © 1996-2017 Alexander Bogomolny
All Rights Reserved.


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