The Spiral Geometry — Global Geometric Structure of the Universe

THE SPIRAL GEOMETRY — GLOBAL GEOMETRIC STRUCTURE OF THE UNIVERSE This work presents a geometric construction based on the hypothesis that the spiral constitutes a fundamental structure for the integrated description of space, matter, motion, gravity, and time. The formulation starts from a geometric architecture composed of a spiral, two intersecting central lines, four 90-degree quadrants, and a three-dimensional extension associated with the z coordinate and the temporal parameter t. The basic spiral representation is expressed as r(t,θ) = a(t)e^θ, with the coordinates x = a(t)e^θ cos θ y = a(t)e^θ sin θ, establishing a dynamic structure in which radial expansion, angular rotation, and temporal evolution can be represented within a common geometric construction. The work develops a structural interpretation in which spiral geometry functions as an organizing element for the relationships among center, expansion, rotation, curvature, trajectory, and transformation. The construction is extended to a three-dimensional representation, allowing the dynamics in the xy plane to be related to the z coordinate and the temporal parameter t. The study further investigates the possibility of interpreting different physical phenomena through a common geometric architecture, establishing relationships among spirality, rotational motion, gravity, propagation, structural organization, and temporal evolution. The construction presented here is theoretical and geometric in nature. Its purpose is to explicitly formulate a mathematical and conceptual structure for investigating physical phenomena traditionally described through distinct mathematical frameworks. Keywords: spiral geometry; geometric structure; geometry of the universe; spacetime; gravity; motion; rotation; spiral dynamics; three-dimensional geometry; time; mathematical structure; theoretical cosmology; dynamic geometry; geometric model.