Sangbun Vector Geometry: A Geometric Construction Framework for Vector Generation

This work introduces Sangbun Vector Geometry (Sangbunhak), a geometric framework in which vectors are generated through chained geometric constructions at a single point on a line or curve. Unlike classical vector theory, which defines vectors as coordinate displacement, this framework defines a vector as an emergent result of accumulated geometric operations including tangent construction, normal projection, circular relations, rotational transformation, and vector composition. The method reveals a dual-structure vector system combining linear geometric components (tangent–projection structure) and rotational geometric components (circle–rotation structure). The construction is stepwise and diagram-driven, allowing intuitive geometric interpretation of vector formation. This upload presents the foundational theory and construction principles.