- The Washington Times - Sunday, February 9, 2003

The father of geometry, Euclid, spent his days coming up with axioms and postulates destined to forever frustrate the modern high school student. Studying lines, planes and a wide variety of figures, the Greek mathematician put forth 467 propositions explaining plane and solid geometry that are still used and expanded upon today.

His work has been translated into animated knowledge in a Web site created by a teacher who lives in the land of the Incas and works hard to educate as well as fascinate.

Geometry: Step by Step

Site address: http://agutie.homestead.com/files/index.html


Geometry and computer teacher and Web designer Antonio Gutierrez, who lives in Lima, Peru, financially supports and maintains the site.

Creator quotable:

"I created this Web site to share my experience as a geometry student, teacher, tutor and parent and my experience as an information-technology professional (programmer, analyst, Web designer and trainer) with anyone who is interested in Euclidean geometry. I am happy to encourage people to enjoy geometry, taking advantage of animation and sound that the Internet offers," Mr. Gutierrez says.

Word from the Webwise:

After paging through the 16 theorems explained mainly in an animated "click, watch and learn" environment, I remembered why I hate geometry.

The site presents two faces to visitors: It uses detailed illustrations and formulas to capture the attention of students fighting with chords, centroids or circumcenters, and it also displays bright colors and shapes for the casual visitor who just wants to know why things look cool. This divide translates into sections for visitors who sort of understand and sections for visitors who like to look at all the pretty drawings and symbols. The hard-core visitors will concentrate on the Problems and Quizzes sections.

Typical problem proofs range from the midpoint revelations of the Butterfly Theorem to something about quadrilaterals and squares called Van Aubel's Theorem to proving the three points of intersection of the adjacent trisectors of a triangle form an equilateral triangle (more commonly called Morley's Theorem).

Quizzes can involve simply dragging an answer over a square to match general geometric concepts or answering difficult fill-in-the-blank questions or solving multiple-choice conundrums to prepare for the math portion of the SAT.

My eyes glazed over after looking at the above sections, meaning I fell into the cool demographic and immediately looked for relief in the Inca Geometry and Quotes sections.

The first features examples from Mr. Gutierrez's home base and includes a look at trapezoids found in the mysterious city of Machu Picchu, the stone of 12 angles found in the ancient Inca Empire capital of Cuzco, and a short explanation of the knotted cords used by the Incas to store information about their culture and civilization, called the Quipu.

Quotes, of course, offered 25 inspirational nuggets about geometry. My favorite, from Isaac Newton, says, "It is the glory of geometry that from so few principles, fetched from without, it is able to accomplish so much."

Ease of use:

Visitors will need a current browser, the Macromedia Flash plug-in and a brain for optimal viewing. Those unable to secure a brain will want to look at the Top Ten Reasons to Enjoy Geometry animation to see a really pretty picture.

Don't miss:

Painter Theodore Gericault's 1818 work "The Raft of the Medussa," does little to help the geometrically challenged, but Mr. Gutierrez offers the history of the work under the Inspiration link as an interactive exploration of how human beings deal with adversity. It should give students a breath of fresh air as they take a break from problem-solving.

Family activity:

The whole clan should plan a visit to a museum and look at how many ways geometric design has influenced everything from ancient ruins to intricate jewelry to artwork over the past 3,000 years or so.

Cyber-sitter synopsis:

Students in high school and college will appreciate the detail and Mr. Gutierrez's love for the subject, but most visitors will look elsewhere for simpler discussions on geometry.

Overall grade: B

Remember: The information on the Internet is changing constantly. Please verify the advice on the sites before you act to be sure it's accurate and updated. Health sites, for example, should be discussed with your own physician.

Have a cool site for the family? Write to Joseph Szadkowski at Webwise, The Washington Times, 3600 New York Ave. NE, Washington, D.C. 20002; call 202/636-3016; or send an e-mail message (jszadkowski@washingtontimes.com).



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