Looking back on their school careers, many people have fond memories of certain subjects. Whether it’s the challenge of history or the enchantment of literature, nearly everyone can point to such highlights. For many, however, mathematics is a subject more to be endured than loved, and more to be respected and feared than admired.
For Melanie Volz, though, math is just plain fun.
“Numbers are like a universal language,” the Wantagh High School sophomore said. “Everyone understands the basics: one, two, three. The fun comes from understanding the secrets behind the numbers.”
One secret Volz spent time pondering over the past year was a sequence explained by the 13th-century Italian mathematician and scientist Leonardo Bonacci, otherwise known as Fibonacci. In the so-called Fibonacci sequence, each number consists of the sum of the two preceding numbers: 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, and so on.
Volz explained that the Fibonacci sequence has been discovered in fields as diverse as botany, where the distribution of sunflower seeds follows a phenomenon known as the Golden Spiral; game theory and political economy, where it is used to predict human behavior; and epidemiology, where it is used to identify genetic anomalies. It can even apply to language: The earliest descriptions of the sequence were used to analyze long and short syllables in Sanskrit poetry.
Fibonacci and DNA
Volz studied DNA in Advanced Placement biology. Building on some of the work done by Luke Hutchinson, of the Sorenson Molecular Genealogy Foundation, on the relationship between Fibonacci numbers and X-chromosomal linkages, she charted some of the ways genetic markers, or matrilineal characteristics, could easily be tracked. Among the characteristics she noticed were the correlations between Fibonacci numbers and the measurements of DNA molecules themselves. Then she explored “X-chromosomal linkages that occurred in a Fibonacci way,” she said.
This means that genetic markers or characteristics inherited from your mother and her ancestors can be identified using the Fibonacci series. “So you don’t have to know who your great-great-great-grandmother was” or her health history, Volz explained. Using Fibonacci sequences can offer an estimate of where to look in a family’s history for abnormalities — or even for such traits as pattern baldness. “You just do the math behind it,” she said nonchalantly.
Volz’s project has implications for both genetic research and epidemiology, she said — possible subjects for her future research.
Although she claims she had no favorite subjects in her early years, it becomes clear as she recounts her progress through school that her ability in mathematics blossomed early. “My mom said, ‘You don’t know how you’re going to come out in life, so you have to be good at everything.’” Melanie recalled the Mad Minutes quizzes from her elementary school years, in which students were asked to solve as many basic problems in arithmetic as they could in a minute or less. She told her mother that she found it frustrating that she couldn’t complete the list of problems in the allotted time. “She heard me and wanted to help me accomplish this goal, so we practiced these small, little competitions.”
Eventually, Volz was successful. But, her curiosity piqued, she began looking for different ways to solve the problems. “That’s where math started to grow on me,” she said.
She doesn’t like to think of her abilities as more advanced than her classmates. “A lot of the time, I don’t even see the problem correctly, and then someone else will say, ‘Do it like this.’ I’ll say, ‘Oh that’s right!’” Like one of her heroes, Albert Einstein, she says it’s not so much that she’s better at math, but rather that she thinks about her problems longer and from more points of view.
Her teachers are not so reticent in their descriptions of Volz’s abilities, however. “I really want to emphasize that she came up with this [Fibonacci] project completely on her own,” science teacher John Sotiriadis said. “We [math and science teachers] were just a sounding board … we offered a couple of small changes. The rest was all her.”
Teachers have encouraged Volz to enter her project in a number of fairs and competitions, including this year’s Al Kalfus Math Fair at Hofstra University, March 1-April 12. Although she was unable to attend to present it in person, it won praise from the judges for both the elegance of the solution and the promise of the contestant.
Volz also submitted the project to this year’s Long Island Science Congress, on April 10; awards will be announced on May 20. And she took part in the Long Island Regional Envirothon at Old Bethpage Restoration on April 30 after press time.
“It’s a series of math and science problems,” Sotiriadis said of the Envirothon, “and the teams have to be prepared to solve them, like an obstacle course. This is where Melanie really shows her value, because she’s got the math ability along with her science.”
SUNY, Hong Kong and Oxford
As a freshman, Volz was accepted into the Institute for Creative Problem Solving, sponsored by SUNY Old Westbury. “We meet every Saturday and listen to guest lecturers on topics like topology or physics,” she said. She was also accepted by Johns Hopkins University’s summer Center for Talented Youth. This enabled Volz, who is fluent in Cantonese, to study at the University of Hong Kong last summer, where she followed a course entitled Paradoxes and Infinities. Among other things, she learned that “infinity is more of a concept than a number,” she said.
This summer, she will spend several weeks following a program in Law and Society and Neuropsychology at Pembroke College, part of the University of Oxford in England. She is interested in game theory, which shapes much of the current research in human behavior in society, as well as neuropsychology,
as possible fields for professional
work, although, she said, “I can’t really think about anything more than a year from now.”
No one else in her family is a standout at math or science, Volz said. An only child, her father, who died when she was 10, was a computer engineer, she said, but her mother’s main talent as far as math goes is as her No. 1 fan.
Unsurprisingly, Volz is taking a full range of Advanced Placement classes, including math, physics (both 1 and 2) and biology. She is also a member of the WHS Minds and Matter Club, which focuses on classmates’ mental health, and the Tri-M music honor society. She plays clarinet in the high school wind ensemble.
She has a newfound interest in graphic arts as well. “I took a class in computer graphics,” she said, “and I really like line art, where you see if you can draw an object just using a single line.
As her interview with the Herald wound down, Volz was eager to return to math class. Sotiriadis laughed and said, “What for? You’re already three chapters ahead of the rest of the class.” It is apparent that her teachers and the district’s science adviser, John Watson, regard her more as a peer than as a student. Sotiriadis indicated that some of Volz’s work was already approaching the far edge of his ability to understand. Melanie and her teachers speak simply of a future where the highest achievements in math and science are realistic possibilities for her.