Browse real student projects, abstracts, and awards.
ISEF · 2021
Mathematics
The contents of the partial fractions contained in high school textbooks are presented in the form of formulas, and there is no explanation of the meaning. When we learn mathematics, formula…
ISEF · 2021
Mathematics
Li-Yorke theorem shows for a continuous self-mapping in interval, if it has a period-3 point, it will have period-n point with any positive integer n. Therefore, period-3 point is worth expl…
ISEF · 2021
Mathematics
The crossing number cr(G) of a graph G is the least number of edge crossings of a plane drawing of G. Determining the exact crossing number of a graph is NP-Complete. In this project, we pre…
ISEF · 2021
Mathematics
Quadratization is a transform of a system of ODEs with polynomial right-hand side into a system of ODEs with at most quadratic right-hand side via the introduction of new variables. It has b…
ISEF · 2021
Mathematics
Euler numbers E_n appear in many places of classic analysis, combinatorics, and topology. They can be defined as Taylor coefficients of the function tanh x + sech x or (in the terminology of…
ISEF · 2021
Mathematics
A graph represents a group of objects (network) and the relations between them. This research introduces ranking of vertices – a mathematical concept, applied to various areas (Google search…
ISEF · 2021
Mathematics
The purpose of this paper is to express Robinson-Schensted correspondence in two different ways, Schensted’s algorithm and a geometric interpretation by Viennot, and compare and prove differ…
ISEF · 2021
Mathematics
Closed geodesic lines on polyhedra are defined as locally shortest polylines not passing through vertices. In 2002 it was proven that the majority of convex polyhedra are free of simple (non…
ISEF · 2021
Mathematics
It is known that attempts to solve some equations and systems of equations by standard methods often cause great difficulties. However, it is more convenient to solve these equations and sys…
ISEF · 2021
Mathematics
Okamoto-Uchiyama encryption scheme is one of the Paillier cryptosystem’s foundations. Unfortunately, its “twin” signature scheme, properties and specialized kinds of digital signatures are n…
ISEF · 2021
Mathematics
After doing a survey about Math learning of grade 8 and 9 students at our school, we found that the level simulating the interest of students in Math and the ability to solve real-life probl…
ISEF · 2021
Mathematics
Arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others, all on the same side of a straight line th…
ISEF · 2021
Mathematics Fourth Award
We often meet the well-known mathematical means: the arithmetic, geometric and harmonic means. They appear in inequalities, extremum problems, geometric connections. However, the ancient pyt…
ISEF · 2021
Mathematics
The purpose of this project is to analyze whether Gaussian Mixture Model can be used to judge the time of a day and weather in a Monet's Haystack. To achieve this, I use python to transform…
ISEF · 2021
Mathematics Fourth Award
Motivated by the characterization of symmetric monoidal functors between Deligne categories, the additive monoid R_+(x) is defined as the set of all nonnegative integer linear combinations o…
ISEF · 2021
Mathematics
This research aims to find strategies to solve the following problem: the minimum number of ant-sucking machines which are needed to guarantee the capture of all ants on an m by n grid graph…
ISEF · 2021
Mathematics
This essay aims to understand the basics of the four color theorem, why it was so hard to prove, and why false proofs failed to prove the theorem. The four color theorem states that a map ca…
ISEF · 2021
Mathematics
The purpose of this project is to determine if it is possible to effectively use traditional regression models to predict an event whose outcome has historically been unpredictable. In our c…