Mashrafi Geometric Model (MGM): A Unified Framework for Vertical–Horizontal–Diagonal Relationships

Abstract

The Mashrafi Geometric Model (MGM) introduces a unified analytical framework for understanding vertical (V), horizontal (H), and diagonal (D) relationships in orthogonal two-dimensional geometry. While classical Euclidean geometry treats diagonal lengths, angles, and slopes as separate formulations, MGM integrates them into a single ratio-driven system governed by the dimensionless parameter .
Using this proportional identity, MGM derives a generalized diagonal equation and complementary angle relations, enabling deterministic geometric behavior once the ratio is known. The model establishes a case-based geometric classification and offers direct applicability to structural engineering, robotics kinematics, signal alignment, and spatial modeling. MGM represents a formal, named geometric contribution and provides a scalable foundation for future theoretical extensions.