Cut The Knot! is a rich and wonderful collection of mathematical miscellany designed to entice the reader to experience mathematics at its delightful best. Alexander Bogomolny has developed an extensive collection of mathematical materials including many interactive java applets of his own creation. The main topical content areas are Games and Puzzles, Arithmetic/Algebra, Geometry, and Probability; these are accompanied by other sections on Interactive Activities, Proofs, Math as a Language, Eye Opener java applets, Analog Gadgets, Did You Know?, Things Impossible, and the CTK Exchange, a discussion forum for math students, faculty, and aficionados. In addition, there is an excellent collection of links to other math resources with accompanying annotations. This site is highly interactive and one can sense the author?s fascination with mathematics and his desire to convey this to his readers. The main page also features over sixty articles from the author?s monthly math column. Please see these related reviews:
This is a resource collection of textual materials along with a multitude of interactive java applets, some avi movies, and an open discussion forum.
Almost any mathematical education endeavor could be facilitated by material on this site.
A basic browser is all that is required to view the primarily textual material; a java-enabled browser is needed for the interactive java applets. The ability of the applets to run on different operating systems and browsers is highly variable with particular difficulties on older Macs and older versions of browsers. MacRuntimeJava2.1 may need to be installed independently of the older Mac OS and there still seemed to be difficulties with Explorer 5. Some failures resulted in particularly nasty system freezes.
Identify Major Learning Goals:
The primary goal is to help readers experience mathematical topics in a positive and interactive way and to help them learn to appreciate the beauty of math. In addition, in the author?s words, ?Learning starts from wondering, and another purpose of this site is to serve as a resource for things, simple but curious, related to Mathematics.?
Target Student Population:
The materials here cover a wide range of topics and ability-levels. The simpler topics in Arithmetic are suitable for Elementary/Middle school students while more advanced topics are at high school and/or college levels.
Prerequisite Knowledge or Skills:
Prerequisite skills vary from basic math knowledge to college-level math knowledge, depending on the topic. All of the material is presented in an accessible manner and the many java applets invite exploration and discovery.
Evaluation and Observation
The content here is of the highest quality?the textual material is thoroughly and accurately conveyed and the numerous java applets are well designed and accompanied by excellent solution descriptions including extensions and applications in related fields. References to original sources are presented and credits are given to individual puzzle-solvers. The author is an accomplished educator and software developer and has combined these talents to create an outstanding mathematical resource. He is an invited author/contributor on the Mathematical Association of America?s web site and authors a monthly column entitled ?Cut the Knot!? An archive of the column is included on the Cut the Knot! site. This site has won dozens of national and international awards for excellence.
Potential Effectiveness as a Teaching Tool
The emphasis of this site is on teaching and learning and the author makes every effort to engage the student/reader in the exploration and discovery process; the level of interactivity is outstanding. Thoughtful solutions are presented and the reader is guided to an analytical understanding of the underlying mathematical principles involved. In some instances alternative solutions are presented; in others, applications to other mathematical fields are described. Altogether, this site contains a wealth of educationally effective materials. In addition, there is an annotated listing of other math resources on the internet that is quite excellent and potentially helpful to the reader. Suitable for many different levels of user - some material is beyond the general user and requires college-level math knowledge. The banner ads at the top of each page and the shopping links in the sidebar are relatively unobtrusive.
Ease of Use for Both Students and Faculty
The site has a very simple and effective design with general navigation bars appearing on every page; the reader is always just a click away from the other site features. The textual materials are interspersed with numerous cross-links that may enrich the reader?s experience. The internal search feature is quick and easy to use and comes with a thorough set of instructions and general searching tips (particularly nice is the simple toggle between ?all? and ?any? searches). Several areas allow for user interaction, including a guest-book that permits posting and reading of user comments. The CTK Exchange is a moderated forum where users may ask math-related questions and interact with other forum participants; the latest postings appear in a sidebar on the main page. The Glossary feature is good for readers with limited math knowledge and is very nicely written. The author offers a stand-alone version of the site on CD-ROM.
Note comments above concerning difficulties with some combinations of older browsers and Mac operating systems.