The Math Presentation required students to film themselves on a topic that other Mu Alpha
Theta Members might like to see.
FIRST PLACE, $1000 PRIZE:
Elliptic Curve Point Addition
by Kristen Rio LaVigne, Stanton College Preparatory School in Jacksonville, FL.
Brief Description: This presentation explains how to add points on an elliptic
curve, y2 = x3+ax + b, using the elliptic curve addition law, derives some of the formulas
involved, and explains why the curve under this operation is a group.
SECOND PLACE, $600 PRIZE:
Packaging Efficiency: Significance and Calculation of Maximum Volume of a Rectangular Box
by GaYoung Park, Seoul International School in Seoul, Korea.
Brief Description: This presentation explains how to find the maximum volume of a rectangular box
with a set amount of material using an example. Mathematical concepts such as expansion of polynomial functions,
derivatives, and critical points are used. The Powerpoint also describes the importance of finding and using the
maximum volume of packages.
THIRD PLACE, $150 PRIZE:
New Solutions of Fibonacci's Problem (Note this file is not working yet.)
by Salome Iremashvili, Archil Omanadze, & Irakli Saralidze, Georgian-American High School in Tbilisi, Georgian Republic.
Brief Description: In XIII century Fibonacci solved the following problem : Find a square number which,
being increased or diminished by 5, gives a square number. Fibonacci’s solution is (41/12)^2. In our project we
found general method of finding other solutions. For example, our solutions of the given problem is: (3344161/1494696)^2.
FOURTH PLACE, $100 PRIZE:
by Erik Waintergarten, University School of Nova Southeastern University in Fort Lauderdale, FL.
Brief Description: I developed a way of understanding and accessing the coefficients of a multinomial expansion.
I created a three dimensional model to illustrate a trinomial and quadrinomial expansion. The video explains how one
can extend this idea to multinomial expansion using abstract spaces. I help the viewer extend Pascal’s Triangle to
apply to a multinomial expansion.
FIRST PLACE, $1000 PRIZE (Tied for first, each presentation won $600 and a copy of Mathematica):
Complex Number Exponents of Euler’s Number
by Avinash Inabathula of Hamilton Southeastern High School in Fishers, IN.
Brief Description: This is an investigation of one of the most fascinating formulas in mathematics, Euler’s formula.
The presentation discusses a step by step proof of the formula using the Taylor series and a graphical representation of the concept on the imaginary plane.
Also proven are a few familiar trigonometric identities.
Basic Cryptology
by Tyler Kimbley of Harris County High School in Hamilton, GA.
Brief Description: Explains the use and components of basic ciphers and types of mono-alphabetic ciphers.
SECOND PLACE, $600 PRIZE (Tied for second, each presentation won $300 and a copy of Mathematica):
Mathematically Quantifying Anthocyanin Content in Blueberry
by Justin Mathew of Clarkstown High School South in West Nyack, NY.
Brief Description: This project is an extension of my science research project. It focuses on quantifying anthocyanin pigment
found in fruits like cherries, blueberry, blackberries, and strawberries. The project involves data collected from UV-Spectrophotometry instruments
and an Attenuated Total Reflectance Fourier Transform Infrared Spectrophotometer. The culmination of the project is the development of a formula
that can be used to quickly determine the concentration of anthocyanin pigments (with anti-aging/anti-cancer effects) in blueberry. The procedure
can be applied to a number of other fruits to develop similar formulae.
The Fibonacci Sequence and the Goldens
by Ryan Breaud & Malerie Bulot of Riverside Academy in Laplace, LA.
Brief Description: Our project is an overview of the history and applications of the Fibonacci Sequence
and the Goldens, the Golden Rectangle, the Golden Ratio, and the Golden Spiral.
THIRD PLACE, $150 PRIZE (the presentation won $100 and a copy of Mathematica):
RSA Cryptography: Security for the World
by John de St. Germain & Alexander Tir of Riverside Academy in Laplace, LA.
Brief Description: This presentation explains the basis of the RSA cryptosystem, which involves extensive use of number theory. Slides begin with an overview
of RSA and cryptography before indulging into proofs of basic number theory concepts involved with the cryptosystem. RSA has many applications
in the world and is one of the strongest cryptosystems used by many computer security systems today.
FIRST PLACE, $500 PRIZE:
Cycloid Curves
by Alex Tir & John de St. Germain of Riverside Academy in Laplace, LA.
Brief Description: The properties of the cycloid curve are explored, as
well as other types of cycloidal curves. This includes its properties as a brachistochrone and a
tautochrone, ranged to similar, fascinating curves such as the realeaux triangle.
(This is a Power Point slide presentation without voice over. Clicking on the highlighted
link will allow you to download the file for viewing in PowerPoint.)
SECOND PLACE, $300 PRIZE:
The Mathematics of Music
by Nathan Bradley Duke of Parkview High School in Springfield, MO.
Brief Description: An oral presentation explores the mathematical relationships within the musical
aspects of rhythm, pitch and sound waves.
THIRD PLACE, $200 PRIZE (Three presentations tied for third place):
The Mean Value Theorem for Derivatives
by Anthony Fernandez of Miami Springs High School in Miami, FL.
Brief Description: This is a brief exploration using Geometer's Sketchpad.
Get Better Scores on your SAT
by Sei Masuoka of Winston Churchill High School in Potomac, MD.
Brief Description: Using Statistics, the SAT answer distribution is analyzed for any pattern within the sample data
taken from SAT prep books. Then a couple of guessing methods are proposed based on the analysis and are tested out on
actual SAT tests. (The Adobe Presenter slide show with
voice over has been uploaded for viewing.)
Statistical Analysis of State SAT scores
by Christopher Lee Squitieri of St. George's Independent School in Collierville, TN.
Brief Description: This presentation looks at the amount of money states spend per student on average and compares
this to student results on the SAT. (This PowerPoint presentation may be saved
for viewing. The current copy has some voice over. We are waiting for a corrected copy to be uploaded soon.)
HONORABLE MENTION:
Associated Primes of the Square of the Alexander Dual of Hypergraphs
by Ashok Cutkosky of Hickman High School in Columbia, MO.
While the presentation was
above the high school level we were looking for, Ashok has already won $23,000 in scholarships for this work from the Siemens
Competition.