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Peer Review

Xah's Home Page



Overall Numeric Rating:

4.33 stars
Content Quality: 4 stars
Effectiveness: 4 stars
Ease of Use: 5 stars
Reviewed: Jun 12, 2002 by Mathematics
Overview: Xah provides for each of 31 ``Famous Curves'' (Archimedean Spiral to
Witch of Agnesi) a page with description, formulas, history, and

A similar page is provided for each of 9 ``Methods of Generation''
of such curves, for example Caustics, Envelopes and Inversions.

Type of Material: Text with many illustrations.
Recommended Uses: It would form an excellent supplement to any analytic geometry course.
Technical Requirements: Any browser should work.
Identify Major Learning Goals: 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.

Evaluation and Observation

Content Quality

Rating: 4 stars
Strengths: 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.
Concerns: 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

Rating: 4 stars
Strengths: The site is very engaging and can be used to show students,
literally, ``the beauty of mathematics.''
Concerns: 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

Rating: 5 stars
Strengths: The site is clearly organized and easy to navigate.
Concerns: None.