Project: MultiOptiEdu
Heuristic Model of Number Decomposition by Tabular Representation (MHDN-RT)
Table of Contents
1. Project Introduction
2. The Concept: From Visualization to Algorithm
3. Visual Component
4. Algorithmic Component
5. Usage
6. Project Structure
7. Author
1. Project Introduction
The MultiOptiEdu project offers an innovative approach to the teaching and understanding of numerical relationships. It explores how a simple visual representation, derived from multiplication tables, can be formalized into a powerful algorithm for determining the Greatest Common Divisor (GCD). This project demonstrates the translation of a visual intuition into an effective and adaptable computational solution.
2. The Concept: From Visualization to Algorithm
The central concept of this project is based on the idea that divisibility relationships can be perceived as a pattern in a graph. The algorithm developed is a direct translation of this observation: instead of using complex formulas, it replicates the process of finding common divisors in a numerical way. The MHDN-RT is thus a proof of concept that visual ideas can be the source of algorithmic innovations.
3. Visual Component
This component uses the matplotlib library to generate a mapping of multiplication tables. There are two versions:
visualisation_basique.py : Displays the products of tables 1 to 10 up to 100.
visualisation_étendue.py : Distinguishes between standard multipliers (≤ 10) and extended multipliers (> 10) for more in-depth analysis.
4. Algorithmic Component
This component is the implementation of the Minimalist GCD Algorithm. This Python script is designed to be a standalone tool, asking the user to enter as many numbers as they wish to find their GCD.
Minimalist: Displays only the information relevant to the analysis.
Adaptive: Works with an unlimited number of integers.
Educational: Clearly demonstrates the logic of common divisors before presenting the final result.
5. Usage
Prerequisites
The project requires the following Python libraries:
- numpy
- matplotlib
To install them, run the command:
Bash
pip install numpy matplotlib
How to run
- For the visualization, run the desired script (visualisation_basique.py or visualisation_étendue.py).
- For the GCD algorithm, run the script pgcd_algorithme.py and follow the on-screen instructions. Type / to finish entering numbers.
6. Project Structure
The project is organized as follows:
README.md : This documentation file.
visualisation_basique.py : Code for the basic graph.
visualisation_étendue.py : Code for the extended graph.
pgcd_algorithme.py : Code for the GCD algorithm.
7. Author
Name: ROKO Japheth
Contact: japhethroko@gmail.com
Date: