Special Relativity Seen from the Fifth Dimension: A Geometric Derivation of Minkowski Spacetime from Euclidean Geometry in R⁵

A geometric reformulation of Special Relativity in five-dimensional Euclidean space. Two inertial observers are represented by Euclidean planes hinged on the shared light line; a Lorentz boost is a rigid rotation about that hinge, and the fifth coordinate w = κ(ct−x) is generated by the relative velocity. Unlike Kaluza–Klein-type approaches, where the extra coordinate is compact, here it is an extended, essential dimension. From this construction alone emerge the Lorentz factor, the Minkowski invariant (ct)²−x² as a conserved area, the longitudinal Doppler shift, the velocity composition law and the energy–momentum relation. It does not propose a new physical theory or new predictions, but a geometric reformulation valid in the collinear sector treated here. This record contains both language versions: English (_en.pdf) and Italian (_it.pdf).