Tucked in with the business news of the day was this headline from the December 9, 1996 issue of The Wall Street Journal newspaper: "Teen Math Whizzes Go Euclid One Better." High-schoolers David Goldenheim and Daniel Litchfield had revisited a 2,000-year old challenge from the Greek mathematician Euclid and solved it in a new way. Given an arbitrary segment, the freshmen found a geometric recipe for dividing its length into any number of equal parts. The mathematics community hailed the students' work as "elegant" and "significant."

Goldenheim and Litchfield devised their segment-splitting technique through old-fashioned conjecturing and reasoning. Yet there was nothing traditional about their geometric tools of choice. The duo conducted their experiments without the aid of a compass or even a ruler. Instead, they turned to technology and a new breed of computer software programs known collectively as "dynamic geometry."

At first glance, the...