Interactive Mathematics Miscellany and Puzzles

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This site is for teachers, parents and students who seek engaging mathematics. Many of the topics are accompanied by Java illustrations. There are more than 1000 Java applets. The applets can be licensed by teachers for inclusion in their own pages.

Most recently I have moved the greatest part of the Games and Puzzles section to a separate site CTK Math Games for Kids. This allowed me to switch from the older applet tags to the object tags that are fast becoming common nowadays. This will insure that the applets always run in the most appropriate version of the Java Virtual Machine without the need for my or user intervention.

The applets run in a browser Java addon and also need a few smaller libraries. For this reason, pages that carry applets may take longer to load than the Java free ones. However, the libraries have to be loaded only once: subsequent pages load pretty fast. Also please note that the Microsoft's Internet Explorer (IE) comes with its own Java Virtual Machine (JVM), the software piece which executes Java applets. The Microsoft's implementation of JVM is inferior to the Sun's and lacks certain features needed by some applets. It is recommended for the IE users to upgrade the JVM, which can be done by downloading it from the Sun's site. The installation procedure is virtually automatic.


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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. Arithmetic is where we all start. Taught properly, it's a front door to the power of algebra Algebra and arithmetic are branches of mathematics that grow on the same stem. Algebra is a step ahead. Use it to solve more advanced problems and explain the wondeful and funny arithmetic tricks. Mathematics is really a great fun. There is no wonder that math games and puzzles come in abundance A theory of games in which Nim plays the most fundamental role. 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. Probability is a branch of mathematics that provides tool for the study of random events Mathematics is impossible without logical thinking. However, logic is often thought of as a bracnch of mathematics Fractals are a great invention (or is it a discovery?) of Benoit Mandelbrot that describe most complex phenomena. The word "fractal" is most often encountered in a company of the word "beauty" Besides having an entertainment value, visual illusions often teach us the wisdom of knowing the limitations of our perception Mathematics reaches into the social arena. It helps understand strange result of congressional and presidential elections, divide fairly inheritance, schedule jobs, and what not Even very knowledgeable and clever people make mistakes. Sometimes clever people invent arguments that look solidly logical but contain a flaw, all with the purpose to sharpen students' understanding of the mathematical argument Calculus is a great discovery of Newton and Leibniz. Regretfully, a course in calculus is often the last encounter of students with mathematics You would not believe your eyes when your computer performs real magic Combinatorics is an outgrowth of artihmetic and algebra. Curious and useful results are achieved by counting in different ways Droodles are a kind of problems that are not annunciated explicitly. Before attempting an answer, the student needs to realize what is the question There are math curiosities that are hard to classify