SITE VISIT: Mathematical Wonders

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Science  02 Jul 1999:
Vol. 285, Issue 5424, pp. 7
DOI: 10.1126/science.285.5424.7d

“Learning starts from wondering,” writes mathematician Alexander Bogomolny on his Cut-the-Knot Web site, a recreational math treasure chest with an attitude. The site's rich array of hyperlinked articles, interactive Java applets, problems, and puzzles offers intriguing ways for math students and teachers alike to wonder and learn.

Math toys from bygone eras benefit greatly from the Java treatment. Consider Sam Loyd's “15 Puzzle,” a popular sliding-piece puzzle from the 1880s. The applet allows visitors to try their hand at it while reading about the underlying theory. After mastering the basic version, they can go on to experiment with variations that would be difficult or impossible to construct in the physical world, such as sliding-piece puzzles on Mobius strips, toruses, or Klein bottles. Even experts will find fresh angles on standard classroom topics. Take “Trisecting an Angle,” an elementary method based on sliding a point along a line. Discovered by Archimedes, the trick has been largely ignored in geometry textbooks because it violates the rigid rules for ruler-and-compass constructions. But, 2300 years later, it's perfect for a Java applet.

Bogomolny, who left a professorship at the University of Iowa to work in educational multimedia, also writes a monthly online column for the Mathematical Association of America that's archived here. “My purpose is to help students and teachers change their attitude toward mathematics,” he says. Judging from his guestbook, he's succeeding. “I'm awestruck!” reads a typical entry, by a teenager named Erin Donovan. “For the first time since I was 7 I'm actually excited about math.”

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