Browse real student projects, abstracts, and awards.
ISEF · 2020
Mathematics
We propose a generalization of Artin's conjecture on primitive roots to the ring Z[i] of Gaussian integers. We conjecture that for a fixed positive integer q, every non-zero Gaussian integer…
ISEF · 2020
Mathematics
The problem of finding the largest pi/2-avoiding spherical set first appeared in the AMS monthly journal in 1974. H. S. Witsenhausen asked readers to determine alpha(n)=(|U|)/(|S^(n-1) |), w…
ISEF · 2020
Mathematics
In this paper, I consider the possibility of using graph theory to study alternating knots and links, which we will simply call knots in what follows. Alternating knot can be built from arbi…
ISEF · 2020
Mathematics
Optimization plays an essential role not only in mathematics, but in many related fields such as biology, robotics or transport. This particular research focuses on finding an optimal planar…
ISEF · 2020
Mathematics
Mathematicians have been known to use logic and intuition to prove mathematical concepts. In modern day mathematics, applications have widely expanded into modern technology. The need for mo…
ISEF · 2020
Mathematics
Determining the quickest network route from point A to point B is a common introductory Graph Theory or Combinatorics activity and algorithms such as Dijkstra’s algorithm are effective tools…
ISEF · 2020
Mathematics
In this paper, we investigate the generalized tent maps, whose vertex, left endpoint and right endpoint are (a, b), (0, s) and (1,c) respectively, where 0<a<1, 0<b<=1,0<=<1 and 0<=s<1. Accor…
ISEF · 2020
Mathematics
To apply the method of inversive generation in order to conclude and prove new properties of a strophoid. And also to find connection of a strophoid with other remarkable curves. Hypothesis:…
ISEF · 2020
Mathematics
A wonderful fact called Thurston's geometrization conjecture states that there are essentially only eight three-dimensional geometries. For the last 20 years, there are lots of attempts to d…
ISEF · 2020
Mathematics
Knowledge of small-scale interactions within a group tells us something about the group big-scale interactions. Commonly, one uses graphs to mathematically model and analyze such relationshi…
ISEF · 2020
Mathematics
In our work, we studied closed lattice bands of unit squares in the n×n×n lattice cubes. We wrote a computer program to find all such bands in the 2×2×2 lattice cube. We were able to identif…
ISEF · 2020
Mathematics
In 2011, Anderson and Frazier introduced the theory of generalized factorizations in integral domains, which is based on studying restrictions of the multiplicative operation of an integral…
ISEF · 2020
Mathematics
In recent years social media has evolved from something that helps you keep in touch with relatives or friends to a driving influencer of all parts of life, politics included. Since its firs…
ISEF · 2020
Mathematics
The purpose of this project was to calculate how often each "space” is landed on while playing Monopoly. This would allow me to better my chances of winning each game. The project had three…
ISEF · 2019
Mathematics
Attention deficit is always a confusing disease: the exact causes of this disorder is still unclear. However, the prevalent idea is that genetics is a major factor of ADHD. Based on that ide…
ISEF · 2019
Mathematics
The purpose of this investigation is to identify patterns, if any exist, among primitive Pythagorean triples so that a triple, given an initial value, can be found. Specifically, the researc…
ISEF · 2019
Mathematics
Many functions do not have elementary antiderivatives and different analytical methods to evaluate the definite integral fail. These functions appear in fields such as biology, physics and e…
ISEF · 2019
Mathematics
One-dimensional cellular automata have been studied by looking at morphisms and properties of growth; however, no proof or demonstration has been made to explain these conjectured patterns a…
ISEF · 2019
Mathematics
Divisibility rules which are used to detect divisibility of numbers are memorable and practical rules and methods which are different for each number. A new study has been conducted to impro…
ISEF · 2019
Mathematics
How is it possible to calculate the direction of the reflection of an arbitrary ray of light off of a surface existing in any number of dimensions without the use of trigonometry? This proje…
ISEF · 2019
Mathematics
The purpose of my research and project is to create a dynamical comprehensive mathematical model that represents the flow of non-Newtonian polymeric fluids through a pipe. For industries fro…
ISEF · 2019
Mathematics
A stock option is a contract that grants the right to buy or sell an underlying stock at a predetermined price. In the United States, almost 20 million stock options are sold every trading d…
ISEF · 2019
Mathematics
The purpose of the experiment entitled “Are MVPs Really the Most Valuable Players?” was to test the accuracy of the sabermetric statistic known as wins above replacement (WAR). To test its a…
ISEF · 2019
Mathematics
Bootstrap percolation, which originated from the field of statistical mechanics, is a class of monotone cellular automata describing an activation process which follows certain activation ru…
ISEF · 2019
Mathematics
Magic squares are defined as matrices whose rows, columns, and main diagonals all add to the same number. They have existed and have been a topic of great interest since as early as 190 BCE,…
ISEF · 2019
Mathematics
This number theory project investigates identities found by multiplying together quaternions in L[x,y,z,w], the Lipschitz quaternions L adjoined with the indeterminates x, y, z, w. Recall th…
ISEF · 2019
Mathematics
Small pieces of plastic from 0.05 mm to 0.5 mm, called microplastics, pollute the ocean by congregating and moving through oceanic currents. Initial regions were defined along coasts to repr…
ISEF · 2019
Mathematics
This project focuses on a contradictory case within the Banach-Tarski paradox. The paradox outlines how any three-dimensional figure can be transformed into any other figure while only using…
ISEF · 2019
Mathematics
Naturally, silkworms construct ellipsoidal cocoons by spinning silk fibers around themselves. When we consider a cocoon in two dimensions, a cocoon has an elliptical shape which is one of th…
ISEF · 2019
Mathematics Fourth Award
I developed a new method to analyze expanding maps with indifferent fixed points. I applied this method to specifically analyze the iterations of the tangent map, proving both measure-theore…