The scene resembles a graduate seminar more than a public high school: A handful of students sit slumped in swivel chairs, so absorbed in the equations on the board that they forget to finish the doughnuts on the table.
The course is mathematical modeling. The problem is to find an equation for building a road that offers the driver a clear view for a specified distance.
The students are on the wrong track and probably won't realize it for a few more days. But instructor Dan Teague says the solving process is the point of the exercise.
"You can really spend a lot of time talking with students about what they're doing and why they're doing it," he said.
For 10 years, teachers such as Teague have been helping make a success out of the North Carolina School of Science and Mathematics, the country's first residential public high school.
Here, juniors and seniors with an exceptional aptitude for math and science are united under one roof for the sole purpose of learning.
The school gives them room and board, teachers with extensive training in their fields and the latest in laboratories and computers. All it asks in return is a commitment to learning, something its students have always been willing to supply.
"This is an environment in which you will find the library packed, every chair taken, until 10:30 at night," said Principal William Youngblood. "Home is school and school is home."
What began as an experiment credited to former Gov. Jim Hunt is moving more into the mainstream a decade later. Today, facilities modeled on the School of Science and Mathematics exist or are planned in Mississippi, Alabama, South Carolina, Texas, Oklahoma, Indiana and Florida.
The school has churned out hundreds of top-notch scientists, doctors, engineers and mathematicians.
Many of its whiz kids win distinction while still at the school, with highbrow awards such as the National Mathematical Contest in Modeling. Three years ago, its students became the first from a high school to place in the college-level contest.
"We keep getting letters from kids who keep saying this was the best educational experience they ever had," Youngblood said. "Many of the students who came to this school tell me it's the first time they've felt they belonged."
Seventy-nine percent of the more than 1,700 alumni contacted in a recent survey already have spent time in graduate school or have plans to do so, he said.
A large majority of alumni also completed their undergraduate college studies at least a year ahead of their peers, he said.
As word of that performance has spread, enrollment at the school has nearly quadrupled to 550. Of the some 900 students who apply each year, only about a third are accepted.
Demographics, in addition to grades, scores and recommendations, play a role in the competition. The school may favor a teen-ager from a poor, rural area, for example, over his rich, city cousin.
Those who make the grade have their work cut out for them. Juniors and seniors often put in 12-hour days. Television is restricted. When they need a break, these kids may take in a Shakespeare play at nearby Duke University.
About 3% eventually decide to return to more conventional schools.
"I don't like science anymore. I'm getting tired," said Jason Parker, half in earnest, as he emerged from a biology class. "It's like it never ends here. You never get done with anything."
But the 16-year-old from Jacksonville has no plans to leave.
"You get to meet a lot of people and get away from home," he said.
For others, it's the challenge that counts.
Laura Poole, 17, of Boone, said the school is the most incredible thing that has ever happened to her. On her desk lies a copy of the print she designed for a T-shirt in art class. "The mind is a muscle," it says.
"You're happier here because you're with more people who are like you," said 18-year-old Brian Sauls of Benson as he tried to debug a computer program that quizzes people on their knowledge of trivia.
Occasionally, a student may get his hands on some alcohol, but the school has few of the problems plaguing most public high schools--no drugs, teen pregnancy or suicide attempts, Youngblood said.
"We don't have knifings in the halls," he said.
Instead of graffiti, walls bear statements of mind power. "Wonders never cease as long as you never cease to wonder," says a poster in the genetics engineering laboratory.
The school, which also teaches the traditional subjects in addition to math and science, has its critics, who contend that it is draining the brain power of other North Carolina schools.
It also costs the state more to educate these students, about $11,000 apiece by the latest estimate from the state education department, compared to $3,715 per student in regular public schools.
The school tries to repay that debt by sharing its learning experiences, offering seminars that train teachers from other schools in new methods of instruction.
"We can take risks and learn from those risks and take what we learn back to schools," Youngblood said. "It's a grand concept."