Michelle Serban, a senior at Calhoun High School, has been named a finalist in the Junior Science and Humanities Symposium.
Serban and nine other Long Island finalists will now compete in the next round on Saturday, Feb. 20.
The first place winners of each category are the finalists from each area. The ones with the highest average from the remaining first, second and third place winners are designated to complete the finalist group.
JSHS is designed to challenge and engage high school students in science, technology, engineering or mathematics. Individual students compete for scholarships and recognition by presenting the results of their original research efforts before a panel of judges and an audience of their peers.
Her research project is “The Relationship between Factoring Certain Quadratics and the Fibonacci Sequence.”
Her project’s abstract is;
“The Fibonacci Sequence is ubiquitous in nature and plays a role in numerous fields from biology to art. Similarly, quadratic equations are also utilized frequently in mathematics and physics. This paper aims to connect the Fibonacci Sequence and the related Lucas Number sequence with the factoring of quadratic equations. Three types of quadratics will be analyzed: Consecutive Absolute Value Coefficient Quadratic Equations (CAVCQE), Consecutive Even Absolute Value Coefficient Quadratic Equations (CEAVCQE), and Consecutive Third Absolute Value Coefficient Quadratic Equations (CTAVCQE). Previous research has found the presence of consecutive terms of the Fibonacci and Lucas Number sequences in the factored forms of CAVCQE and CEAVCQE. This paper expands upon this research to discover a method of factoring CAVCQE and CEAVCQE using the equation y=0.322+1.04lnx, where x is the second coefficient of the quadratic and y is the lower term number of the Fibonacci and Lucas Number sequences being used in the factored form. The method makes factoring quadratics, especially those with large coefficients, more efficient. CTAVCQE were also found to share a relationship with the aforementioned number sequences and to be factorable using the method discovered for CAVCQE and CEAVCQE. Future research can focus on Consecutive Square Absolute Value Coefficient Quadratic Equations (CSAVCQE) or other quadratics with coefficients that do not have constant differences between their absolute values and can study cubic equations as well. Going into greater depth on the properties of Fibonacci numbers in terms of factoring and other fields will provide a greater understanding as to what this number sequence’s true significance is.”
She is also the 2021 salutatorian for Calhoun.