This site is a collection of geometric derivations and demonstrations of problems from many areas of mathematics including Buffon?s needle problem, an exploration of the catenary, deriving the volume of a torus, a description of the centers of triangles, a look at the Reuleaux Triangle, and an investigation of properties of electrical force fields, to name a few. The author supports his derivations visually using carefully prepared images, Java applets and downloadable Geometer?s sketchpad (GSP) sketches. In cases where derivations are not given (for example the tangent circle applets), the applets are self-explanatory and are suitable for student exploration.
Presentation of the derivation of various facts from geometry, physics, calculus, and algebra.
Target Student Population:
Prerequisite Knowledge or Skills:
Some topics only require elementary geometry. Others (hanging ropes) require even some differential equations to fully appreciate the derivation.
Type of Material:
Java enabled browser and Geometer?s sketchpad to view the GSP sketches.
Evaluation and Observation
Explanations are very well written and are carefully presented in a friendly non-technical manner, avoiding the use of jargon and all-too-deep mathematics when more intuitive methods are available. References and historical background are provided when possible and the illustrations are very helpful. Many lessons include some questions that are excellent for students doing group exploration, while others are suitable for undergraduate research problems. If the reader has Geometer's Sketchpad the nearly 30 downloadable sketches make the site worth it by themselves. These sketches allow visitors to interactively explore some fairly complicated, but very interesting mathematics, as well as being able to see some very useful and intricate GSP constructions.
Potential Effectiveness as a Teaching Tool
This site is an excellent supplement for any textbook covering similar materials and many of the applets could be used for demonstration purposes during a lecture. Readers that use this site will, most likely, find themselves drawn to the other parts. The sense of enthusiasm the author conveys is most certainly contagious.
Some lessons, such as the Chinese Handcuffs lesson, are simply an interesting GSP sketch or java applet together with a list of questions for further exploration. Some of these questions may be (or lead to) problems that are appropriate for undergraduate research.
Other lessons such as the Tangent Circles lesson have interesting questions that many students would never think to ask, such as:
-Why do some configurations have fewer solutions than others?
-Why do some configurations have no solutions?
With its excellent visual presentation of some very interesting and (dare we say) fun problems from several fields of mathematics,
this has site uses that are too numerous to list in one review
Ease of Use for Both Students and Faculty
Aside from the need for GSP the pages read like a well-written text. The applets and GSP sketches were either explained well or self-explanatory. But like any textbook most students will need some guidance through most of these lessons. It seems that all of the Java applets were created using GSP and Java Sketchpad, hence there is continuity to the look and operation of each interactive component. Furthermore, using the Show All Hidden command in GSP, students and teachers alike can discover some of the surprising capabilities of GSP.