Browse real student projects, abstracts, and awards.
ISEF · 2017
Mathematics Fourth Award
This project takes a different approach to meteorological forecasting by investigating underlying patterns in local weather fluctuations and attempting to find a connection between these phe…
ISEF · 2017
Mathematics Third Award
From the world wide web to social networks, big data often take the form of graphs. It is important to be able to generate realistic random graphs in order to analyze the properties of real…
ISEF · 2017
Mathematics Second Award
Number theory is a field where you study integers and the way they relate to each other. We look at a section of number theory called multiplicative functions. These functions act as machine…
ISEF · 2017
Mathematics
This paper provides a generalization of the Calkin-Wilf tree. The Calkin-Wilf tree is an infinite binary tree in which all nodes are labeled by reduced positive rationals and each reduced po…
ISEF · 2017
Mathematics
In the digital age, more and more data needs to be transmitted securely, making cryptographic functions increasingly important. At the basis of all cryptographic functions is a pseudo-random…
ISEF · 2017
Mathematics Fourth Award
We study the distortion of an optimal embedding of a perfect binary tree into a Euclidean space with a fixed number of dimensions. The distortion is a characteristic of the embedding, descri…
ISEF · 2017
Mathematics
It is a fundamental problem to find a good criterion to decide whether a system of polynomial equations has a solution. Hilbert Zero Point Theorem says that for two polynomials f(x,y) and g(…
ISEF · 2017
Mathematics
Mersenne Primes are prime numbers of the form 2^p-1 where p is prime. These numbers have been studied for over 2,000 years and continue to mesmerize mathematicians today with a number of uns…
ISEF · 2017
Mathematics Third Award
This work deals with an open question in math with direct implications to spectral theory and to mathematical physics. A measure describes the distribution of mass over a general set. Given…
ISEF · 2017
Mathematics
Polygon Triangulation problem is one of the problem in combinatorial mathematics. The problem is that, in how many ways can a convex polygon with n+2 sides (labelled 0,1,2,…,n) be divided in…
ISEF · 2017
Mathematics
The field of Diophantine approximation is a branch of number theory which concerns itself with certain properties of real numbers in relation to the rational numbers. In specific, one may de…
ISEF · 2017
Mathematics
The purpose of this project was to determine if an algorithm could be used to quantitatively analyze paintings. It was hypothesized that there would be a significant difference between the p…
ISEF · 2017
Mathematics Fourth Award
In an era of rapid growth in information technology, a significant danger threatens digital security: cyber-attacks. Public-key cryptosystems are used to overcome virtual vulnerabilities. Th…
ISEF · 2017
Mathematics
Given a triangle and a set of three angles, celebrated geometrical theorem of Jacobi (1825) produces a new triangle and a point (Jacobi point) in perspective with the first. Different proper…
ISEF · 2017
Mathematics
In the research we study the systems of tangent circles inscribed in generalized Archimedes arbeloses and its properties. By the generalized Archimedes arbelos we mean one of the following m…
ISEF · 2017
Mathematics
A method of solving of the Diophantine equations of the first degree, that lets us to solve these equations in general already exists. But there are no such methods for the Diophantine equat…
ISEF · 2017
Mathematics
Language is the lens through which humans see the entire world. The purpose of this research project is to observe how the language in which a message is written impacts the time required fo…
ISEF · 2017
Mathematics
In their study of generalized covering maps in categorical Galois theory, Borceux and Janelidze analyzed topological properties of the coproduct completions of small categories. Up to equiva…
ISEF · 2017
Mathematics
In this paper, we focus on the dynamical behaviors of the non-monotone points and the periodic points of the tent mappings under iteration. We first discuss the variation of the number and l…
ISEF · 2017
Mathematics
In this project, we defined a mid-tangent point with respect to a fixed point X and a tangent at a point P on planar curve C as a point on the tangent that is equidistant from X and P. We st…
ISEF · 2017
Mathematics
In many cases of Land Search and Rescue the search for individuals that are believed to be unconscious or in need of medical attention are time critical. However, due to the shortage of reso…
ISEF · 2017
Mathematics
This puzzle was first mentioned in Dudeney’s book “Puzzles of Canterbury” in 1907. Since then an optimal algorithm in the general case has not been obtained despite many attempts from people…
ISEF · 2017
Mathematics
There are numerous mathematical systems that are implemented in the process of archaeological seriation. Archeological seriation is a relative dating process in which assemblages are placed…
ISEF · 2017
Mathematics
The burning number of a graph was introduced by Bonato-Janssen-Roshanbin [Lecture Notes in Computer Science 8882 (2014)] for measuring the speed of the spread of contagion in a graph. Today,…
ISEF · 2017
Mathematics Third Award
Appel and Haken (1977) proved that four colors suffice to color any map by using the discharging method. While the original problem required the same four colors, but what if each country ha…