Number Theory

    

The Octa Quadrant System: an Extension of the Cartesian Coordinate System

Authors: Israr Luqman

This paper proposes the Octa-Quadrant System (OCS), an innovative extension of the Cartesian coordinate system that divides the plane into eight quadrants instead of the traditional four. Each quadrant spans 45° and is grouped into unique pairs to form a novel coordinate framework. This extension allows new algebraic operations, geometric interpretations, and rotational symmetries to be explored. Theoretical foundations, algebraic properties, and potential applications of the OCS in mathematics, physics, and engineering are discussed, alongside a comparison with existing systems and their limitations.

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[v1] 2024-12-22 03:27:51

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