Browse real student projects, abstracts, and awards.
ISEF · 2025
Mathematics
This project investigates the representation of polygons through the roots of unity. Since the points in the complex graph of power functions lead to equidistant solutions, they can then be…
ISEF · 2025
Mathematics
Lothar Collatz defined a function on natural numbers: divide x by 2 when it is even, multiply by three and add one otherwise. He conjectured that repeated application of this function to any…
ISEF · 2025
Mathematics
The smooth sliceness of a knot is an important property with connections to longstanding problems in topology such as the smooth four-dimensional Poincare Conjecture (4SPC) and the Slice-Rib…
ISEF · 2025
Mathematics
We propose a gated neural framework for solving partial differential equations (PDEs) of the form L(u(x)) = f(x), where x ? O ? Rn and u : O ? R. The solution u(x) is expressed as a residual…
ISEF · 2025
Mathematics
This study aimed to develop a theorem that algebraically calculates the maximum number of spheres inscribed within a ring torus and its resulting total volume. A ring torus is a circle with…
ISEF · 2025
Mathematics
For a polynomial P(x) with integer coefficients and a maximum positive integer root m, we consider the product of its values from x=m+1 to n and denote it as Fp(n). Building up on previous w…
ISEF · 2025
Mathematics
We explore the Euler-Lagrange equations in which tangent spaces have non-coordinate bases. This generalized form is the Boltzmann-Hamel (BH) equation, which contain a term dependent on a coe…
ISEF · 2025
Mathematics
This research aimed to explore the behavior of particles in high-energy proton collisions through a Markovian model to identify cohesive patterns and predict particle behavior. One fundament…
ISEF · 2025
Mathematics
Understanding whether selfish or altruistic behavior benefits an individual more remains challenging using traditional approaches like studying human samples. The prisoner's dilemma, a game…
ISEF · 2025
Mathematics
Polygons, a fundamental concept within the sub-learning area of geometry, have a versatile structure that makes them highly suitable for generalization. With applications extending across ma…
ISEF · 2025
Mathematics
There are over 400,000 cases of Sudden Cardiac Arrest (SCA) recorded annually, with over 90% of these events being fatal. The current detection system used to detect cardiac arrest in hospit…