Browse real student projects, abstracts, and awards.
ISEF · 2020
Mathematics
We present a polynomial-time approximation Algorithm for the 3-Peripatetic Salesman Problem on maximum (3-PSP-max). The m-Peripatetic Salesman Problem (m-PSP) is a generalization of the clas…
ISEF · 2020
Mathematics
Traffic models are fundamental to our ability to deal with traffic congestion in the modern world. Locating traffic congestion points are beneficial as the Government can find solutions to d…
ISEF · 2020
Mathematics
The classical method of stars-and-bars is used to count the number of ways to place identical items into distinct bins, but is not applicable when the bins are also identical. The aim of thi…
ISEF · 2020
Mathematics
In this project we set out to prove that in isosceles triangles The medians, heights and bisectors are equal. The two line segments – formed from connecting the bases of medians, heights and…
ISEF · 2020
Mathematics
This study aims to find a solution to non-perfect square roots. The new Algorithm gives an approximate result by which we can identify the error percentage using the following equation: Erro…
ISEF · 2020
Mathematics
Robin’s criterion states that the Riemann hypothesis is equivalent to sigma(n) < exp(gamma) n log log n for all integers n > 5040, where sigma(n) is the sum of divisors of n and gamma is the…
ISEF · 2020
Mathematics
We examined the iteration of the mapping that is given by Vieta's Theorem. Under its application different behaviours like convergence and divergence emerge. We could prove that the converge…
ISEF · 2020
Mathematics
The Collatz Conjecture can be written as a single-part function using indicator functions, and extending it to the complex plane allows for it to be graphed as a fractal. The indicator funct…
ISEF · 2020
Mathematics
We consider regular n-gons, free to float in 2D space. This allows them a rotational property. Now, we consider the problem of calculating the number of distinct a-colorings of its vertices.…
ISEF · 2020
Mathematics
Mathematical modeling is a powerful way to comprehend emerging properties/behaviors in social problems involving many parameters acting simultaneously and non-linearly. Current epidemiologic…
ISEF · 2020
Mathematics
Different people suit best in different glasses. In order to allow more people to get best fit glasses with less money in less time, this project explores the mathematical relationship betwe…
ISEF · 2020
Mathematics
The El-Gamal digital signature scheme (or its modifications) is a core for many modern cryptographic standards, but most of known attacks do not consider generalizations of this scheme. The…
ISEF · 2020
Mathematics
In the abelian sandpile model, recurrent chip configurations are of interest as they are a natural choice of coset representatives under the quotient of the reduced Laplacian. We investigate…
ISEF · 2020
Mathematics
In this paper, we study the question of asymptotic degrees of freedom in a viscous flow. Particularly, we create a bound on the dimension N of the determining node set xi of a fluid with tim…
ISEF · 2020
Mathematics
A k-derangement is a special kind of permutation of n objects, such that no subset of size k from the n objects is invariant. A 1-derangement is a permutation that has no fixed points. Count…
ISEF · 2020
Mathematics
My project is in the area of sports analytics and it aims to understand soccer movement. I use two data sets. One is a public data set of professional soccer possessions that contains time s…
ISEF · 2020
Mathematics
In the past, many researches on the pricing of movie tickets have only given some subjective suggestions and there’s no mathematical expression, however, starting from the consumer choice be…
ISEF · 2020
Mathematics
Finite group actions on closed orientable surfaces via homomorphisms is a widely studied topic in group theory and low dimensional topology. It is closely related to symmetries of surfaces a…
ISEF · 2020
Mathematics
In modern world due to pollution and other reasons people started to look for a planet which can replace Earth. I started to research about it aswell. I have worked on planet Kepler 452b whi…
ISEF · 2020
Mathematics
Graphs are defined as a set of vertices and a set of edges consisting of unordered pairs of vertices. They can be used to model many real-world structures, systems and especially networks. T…
ISEF · 2020
Mathematics
A Gray Code sequence is a set of 2^n binary numbers in which only one bit changes between two consecutive elements and this property helps in reducing errors in data transmission in hardware…
ISEF · 2020
Mathematics
In our project, we create a virtual GeoMir, the inhabitants of which are polyhedrons, as well as virtual organisms, which we called ?-rodents. ?-rodents are able to build straight lines, as…
ISEF · 2020
Mathematics
Primes are the building blocks of composite numbers. One day I gifted a mathematical property of the birthdate (9) of one my friend as a birthday present, I observed a unique and interesting…
ISEF · 2020
Mathematics
We Wanted tot determine hoe many tries it would take for probability to be accurate. To determine this we used a full deck of playing cards without the two jokers; so a total of 52 cards. We…
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…