## Differential Geometry

Fundamental Theorem of Space Curves Visualization

In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size) completely determined by its curvature and torsion.

Given curvature and torsion , the Frenet equation relates the tangent, normal, and binormal vector of the curve at each position.

## Linear Programming

Simplex Algorithm

I have coded recently the simplex algorithm. It is an algorithm that solves the optimizations of a problem of linear programming. It gives a function to minimize and constrains the variables with an inequality form.

It can be proven that the simplex algorithm solves this problem in Non-Polynomial time.

## Connect 4 AI Solver

Recurrent algorithms C++ and Python

I have been working on recurrent algorithms. They’re a bunch of examples in which you can implement these algorithms. However, we usually see that they are efficient.

Connect 4 is a simple game that can be easily programmed and solved to win every time. I have made in Python an AI that solves and wins. It is not programmed in C++ because I wanted a GUI.

## Dynamic Systems

N-Order Linear Systems

I have done a project for my math class where we analyze the linear systems. We have classified the first and second-order linear systems and give a general formula for an n-linear system. We have used algebra notation and we have encountered with the companion matrix power to the n problem.

The n-linear systems are used widely in finance for loans, interests, etc.