Search past science fair projects

Origami Knots

Mathematics

Both knot theory and origami have many relations to mathematics and the overall broader scientific world. The main problem in mathematical knot theory is identifying knot equivalence. In thi…

Perfect Triangle Research and Exploration of Expansion to Four Dimensions with Using Code Design

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…

Period-3 Point of Generalized Tent Mapping: Orbit Type and Stability Analysis

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…

Proposal for an Algorithm for Finding the Crossing Number of a Graph

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…

Quadratization of ODEs: Monomial vs. Non-Monomial

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…

Ramanujan Congruences for Tangent Numbers

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…

Ranking of the Vertices in a Weighted Graph

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…

Robinson-Schensted Correspondence and Standard Young Tableaux

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…

Simple Closed Geodesic Lines on Catalan Solids

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…

Solving Some of the Algebraic Equations Using Trigonometry

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…

Specialized Digital Signatures Based on the Paillier Cryptosystem

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…

Stimulating Mathematical Thinking Through the System of Geometric Exercises and Games Designed by Scratch Programming

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…

The Arbelos in Three-Dimensional Space and the Archimedean Spheres

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…

The Contraharmonic Mean: Connections, Relations to Number Theory, Possible Generalizations

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…

The Mathematical Analysis of Claude Monet's Impressionistic Masterwork —Haystack

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…

The Structure of the Positive Monoid of Integer-Valued Polynomials Evaluated at an Algebraic Number

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…

Turning Grids into Forests

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…

Understanding the Four Color Theorem and Attempts to Prove It

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…

Using Advanced Predictive Modeling in a Nontraditional Discipline - The NFL Draft

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…

CSEF 2021 project J1405 — title not published

Mathematical Sciences Second Award

CSEF 2021 project J1407 — title not published

Mathematical Sciences Honorable_mention Award

CSEF 2021 project J1409 — title not published

Mathematical Sciences Fourth Award

CSEF 2021 project J1410 — title not published

Mathematical Sciences Third Award

CSEF 2021 project J1413 — title not published

Mathematical Sciences First Award

CSEF 2021 project J1414 — title not published

Mathematical Sciences Honorable_mention Award

CSEF 2021 project J1416 — title not published

Mathematical Sciences Honorable_mention Award

CSEF 2021 project S1407 — title not published

Mathematical Sciences Honorable_mention Award

CSEF 2021 project S1409 — title not published

Mathematical Sciences Third Award

CSEF 2021 project S1411 — title not published

Mathematical Sciences Second Award

CSEF 2021 project S1414 — title not published

Mathematical Sciences Honorable_mention Award