Kang Ying "Connie" Liu digs anime, likes to sketch and paint, enjoys a good hike and has been known to play a little piano. Classmates like her. So do her teachers.

So to heck with Aristotle and his notion that genius is always attended by a tincture of madness. Cast away all those preconceived, pop culture-fed images of math prodigies as beautiful but unstable minds.

Liu, 17, has a gift. That much was readily apparent to the judges at this month's Hawai'i State Science and Engineering Fair, who examined Liu's original work on triangle inequalities with a mixture of awe and giddy excitement.

But those close to the St. Andrew's Priory student insist that Liu's best attributes are her feet-on-the-ground demeanor and uncontrived humility.

All will be on display next month when Liu joins 21 other exceedingly bright Hawai'i students at the Intel International Science and Engineering Fair in San Jose, Calif.

Liu earned her all- access pass to the prestigious event by divining nine new geometric formulas for describing triangle inequalities.

One of the judges at the Hawai'i event, University of Hawai'i math professor J.B. Nation, said he had not seen such an accomplished display of abstract math at the fair in more than 30 years.

In Euclidian geometry, it is understood that if you add any two sides of a triangle, their combined length will be greater than the length of the remaining side. That is the theorem of "triangle inequality."

In the mid-1st century A.D., Heron of Alexandria devised a formula — Area = SQRT(s*(s-a)(s-b)(s-c)) where s = (a+b+c)/2 — for determining the area of a triangle, as defined and limited by the theorem of triangle inequality.

While these basic understandings, and a host of related formulas, have proved reliable (if challenging to the left-brain deficient), in Liu they sparked a curiosity and, later, a sense of challenge.

Liu, who came to Hawai'i from Taiwan two years ago, said she suspected that she could find simpler ways to describe triangle inequality. And so, for the better part of one year, she read as much as she could on the subject and experimented with different approaches.

"She got it in her mind that there was a simpler way so she just investigated and worked her way through it," said Michael Grech, Liu's chemistry teacher and adviser.

POST-GRAD SKILL

The result was a breakthrough formula that yielded a series of variations, each charting uncharted waters of geometry. Outside analysis confirmed that at least three of Liu's formulas produce results more accurate than previous formulas.

"Every one can apply to any triangle," Liu said.

Nation said he was amazed at the work Liu had accomplished at such a young age.

"This is the sort of thing we ask our graduate students to do for their M.A.s or Ph.D.s," Nation said. "What I was most impressed with was when I asked her what motivated her and she said she wanted to see if she could come up with a new way of doing this. That's what we try to motivate our (UH) students to do.

"She didn't need anyone to motivate her."

Nation said he posed a series of difficult questions to Liu to see how well she understood her subject.

"Her answers showed that she didn't just know the facts but she had a deeper, more thorough understanding than anyone," he said. "The way you get results is by looking at a thing and understanding it better than anybody else. She understood it better than I."

Grech said he first realized Liu's potential when she aced her second chemistry exam, a test he had booby-trapped with particularly daunting questions. He said she was the first student in his five years at the school to answer each one correctly.

SAN JOSE NEXT

But Grech's respect for his young student extends far beyond her considerable intellectual abilities and natural curiosity.

"She's an extremely normal, down-to-earth girl," he said. "She's very well-liked by the rest of the students and respected by the teachers."

Liu lives with her mother, a senior counsel stationed in Honolulu. Her father and older brother remain in Taipei.

Liu said she's always had an aptitude for math and science, a natural predisposition she is all to happy to stoke.

"I like math because there is an absolute answer to it," she said.

Liu is preparing for the International Science and Engineering Fair by streamlining her display and practicing her delivery. She said she's eager to meet other young scholars in San Jose, and is excited at the prospect of vacationing in Taiwan over the summer.

Because while she enjoys her life in Hawai'i, even prodigies need comfort food.

"I miss the food," Liu said, laughing. "There are no good Taiwanese restaurants in Hawai'i!"