Xah provides for each of 31 ``Famous Curves'' (Archimedean Spiral to Witch of Agnesi) a page with description, formulas, history, and applications.
A similar page is provided for each of 9 ``Methods of Generation'' of such curves, for example Caustics, Envelopes and Inversions.
To learn analytic geometry by experiencing interesting examples.
Target Student Population:
High school precalculus students, college students of calculus and analytic geometry.
Prerequisite Knowledge or Skills:
Some skill in understanding 2-variable equations and their graphs. polar coordinates are used in many examples, as are constructions using tangent lines.
Type of Material:
Text with many illustrations.
It would form an excellent supplement to any analytic geometry course.
Any browser should work.
Evaluation and Observation
The graphics are beautiful, plentiful and instructive. The connections between the different curves, via the inverse, involute, evolute, pedal, catacaustic and radial constructions for example, are illustrated whenever appropriate and serve to link one page to another.
The English is irregular in places (this would be very easy to correct), probably not enough to confuse students.
On almost every page, there are links which are indicated as leading to Quicktime animations or Mathematica notebooks, but which instead lead to a page announcing that these enhancements are now available on a CD-ROM version of the website (available for purchase). The CD has other enhancements as well, and is probably a worthwhile purchase for anyone interested in going further into the material on the site, but the links are nevertheless misleading.
Potential Effectiveness as a Teaching Tool
The site is very engaging and can be used to show students, literally, ``the beauty of mathematics.''
The site is presented as a dictionary, i.e. for reference and for exploration. There is no preferred track for students to follow (leading, for example, from simpler curves to more complex).
There are no ``open questions'' or suggestions to students for investigation on their own.
Ease of Use for Both Students and Faculty
The site is clearly organized and easy to navigate.