no3inline

🧩 The No Three in One Line Problem

The "No Three in One Line" problem, often referred to as the "No-three-in-line" problem, is a captivating combinatorial geometry puzzle. This problem challenges users to place points on a grid, ensuring that no three points are collinear.

📖 Problem Statement

Given a $(n \times n)$ grid, the objective is to place as many points as possible on this grid such that no three points lie on the same straight line, either vertically, horizontally, or diagonally.

🧠 Historical Context

The origins of this problem date back to the late 19th and early 20th centuries. Over time, various mathematicians have explored this problem, offering solutions, improvements, and generalizations.

🌐 Implications and Applications

While it might appear purely theoretical initially, solutions and techniques for this problem have found applications in numerous areas like:

• Coding Theory: Utilizing geometric configurations for the design of error-correcting codes.
• Finite Geometry: Investigating the properties and structures of finite geometric spaces.
• Design Theory: Crafting designs where specific configurations are avoided.

For a more in-depth exploration of this problem, you can read more about it on Wikipedia.

Installation

🚀 Automatic

pip install git+https://github.com/vjdad4m/no3inline

💼 Manual

1. Clone the repository:

git clone https://github.com/vjdad4m/no3inline.git

• For Linux:

  cd no3inline
  ./buid.sh

• For Windows:

  cd no3inline
  .\build.bat