Browse real student projects, abstracts, and awards.
ISEF · 2018
Mathematics Second Award
Consider a square of integer side N divided into unit squares. The opposite vertices of some unit squares are connected with diagonal lines so that none of the diagonals have common points.…
ISEF · 2018
Mathematics
The Collatz function is defined as follows: start with a positive integer x. If x is odd, multiply it by three and add one, and if x is even, divide it by two. A recursion of this function c…
ISEF · 2018
Mathematics
In classical logic, formulas are constructed using a given alphabet composed of connectives and prime statements. The prime statements are assigned one of two truth values: {t,f} and the con…
ISEF · 2018
Mathematics
Abstract algebra is a branch of mathematics that studies algebraic structures. Lie algebras theory is one of the most important and developing topic of abstract algebra. A Lie ring is a Lie…
ISEF · 2018
Mathematics
In this project, the properties of the bicentric quadrilaterals were examined. Bicentric quadrilaterals are quadrilaterals, which have both a circumcircle and incircle. For this reason, they…
ISEF · 2018
Mathematics Third Award
This project, which is in number theory, explores the connections between quaternions and primitive Pythagorean quintuples. It is known that the square of a Gaussian integer (a complex numbe…
ISEF · 2018
Mathematics
Restoration efforts of wild oysters are often unsuccessful, in that they do not produce a robust population of oysters that are able to successfully reproduce. Furthermore, the dynamics of w…
ISEF · 2018
Mathematics
The machine will help learners with hearing impairment to read cosines,sines and tangents of an angle at the same time to improve mathematical performance in special schools(schools for the…
ISEF · 2018
Mathematics
In 1948, Paul Erdos and Ernst G Straus formulated the Erdos-Straus Conjecture, which states that for any natural number n, the equation 4/n=1/x + 1/y + 1/z is solvable in positive integers x…
ISEF · 2018
Mathematics
Szemerédi's theorem asserts that all subset of the natural numbers with positive upper density contains arbitrary large infinitely many arithmetic progressions. This is the generalization of…
ISEF · 2018
Mathematics
The purpose of this projection was to determine whether the complexity of the stereographic or inverse stereographic projections of prime knots increased as their number of crossings increas…
ISEF · 2018
Mathematics
First, the number of pairs of consecutive quadratic residues modulo an odd prime p are counted, using sums of the Legendre symbol. We then extend this to triples of consecutive quadratic res…
ISEF · 2018
Mathematics
Finsler-Hadwiger's inequality is a classical inequality, which is a stronger version of Weitzenboeck inequality. It connects side lengths and area of Euclidean triangles. The works on Finsle…
ISEF · 2018
Mathematics
The Merriam-Webster dictionary defines a paradox as a "statement that is seemingly contradictory or opposed to common sense and is yet perhaps true." Can napkin rings from spheres of differe…
ISEF · 2018
Mathematics Fourth Award
This project aims to derive the polar equations from relation of the points on the center line of water that swirls from Butterfly sprinkler heads. The water path including the inner rim, th…
ISEF · 2018
Mathematics
Introduction: Geometric problems, which can be solved by using compass and straightedge,were always one of the most unique and beautiful parts of math. Even in ancient Greece active discussi…
ISEF · 2018
Mathematics
This project aimed to build a computer program that contains an interactive underwater ROV (Remotely Operated Underwater Vehicle) build and test simulator. Its purpose was to engage people w…
ISEF · 2018
Mathematics
The ability to tell between truly random numbers and pseudorandom numbers generated by computers is important in many scientific fields and real life applications. Pseudorandom number genera…
ISEF · 2018
Mathematics
Arithmetic is China’s brilliant mathematical cultural heritage. With the using of the method of documentation, the thesis discusses two aspects of, from the introduction of the ancient equat…
ISEF · 2018
Mathematics
The concept of the Euler Line was first published by the Swiss mathematician Leonhard Euler in his dissertation “Variae Demonstrationes Geometriae.” Through inductive reasoning, we discovere…
ISEF · 2017
Mathematics Fourth Award
The chromatic number of the n-dimensional Euclidean space is the minimum number of colors with which the entire space can be colored so that every two points one unit apart have different co…
ISEF · 2017
Mathematics
Capillary floating problem in physics concerns the equilibrium positions of floating bodies whose positions and orientations are governed by capillary forces. It plays an important role in m…
ISEF · 2017
Mathematics
The purpose of this paper is to introduce the reader several unusual areas of mathematics that not many people are aware of. The principles of Latin squares, projective and affine planes can…
ISEF · 2017
Mathematics
Western music is based on two concepts – Harmony, which is the simultaneous sounding of multiple notes (chords), and Voice Leading, which is the temporal motion of these notes (voices). The…
ISEF · 2017
Mathematics
A Method for Analyzing Basketball Teams started as an attempt to use statistics to analyze our team's offense. Eventually it grew into a data collection and analysis software. There are thre…
ISEF · 2017
Mathematics
The problem of points is a historical problem confronted by many mathematicians throughout history. It presents an interrupted series of games and asks the question of how the probabilities…
ISEF · 2017
Mathematics
The internet’s expansion has increased the data available to researchers, allowing analysis to make insights into human behavior. This project statistically analyzes trends in computer scien…
ISEF · 2017
Mathematics
The Collatz conjecture is an unproven conjecture in mathematics; any initial input to the Collatz sequence will give an eventual output of one. The importance of proving the conjecture is du…
ISEF · 2017
Mathematics
This project aims at challenging the underlying conjectures in many modern encryption systems. The problem of integer factorization, and its associated difficulty is solving, is essential to…
ISEF · 2017
Mathematics
In the futuristic dystopia, The Minority Report starring Tom Cruise, the police would be at the crime scene before it occurred. Is this really possible? My project uses data science and mach…