A Geometrical Approach to Neutrino Oscillation Parameters

We propose a geometric framework that reinterprets neutrino mixing as a triangle relation among the three mixing angles. The empirical observation that twice the sum of θ_12, θ_13, θ₂₃ nearly equals 180° motivates the “mixing triangle hypothesis,” in which these doubled angles form the interior angles of a Euclidean triangle. Within this simple construct, the atmospheric angle θ₂₃ becomes geometrically determined by the solar and reactor angles, naturally resolving the long-standing octant ambiguity. When tested against the latest NuFIT-6.0 and PDG-2024 global-fit data, the relation predicts θ₂₃ = (48.0 ± 0.7)°, consistent within 1σ of experiment, while reproducing the observed ratios of mass-squared splittings at the few-percent level. The framework captures the relative hierarchy among neutrino masses but not their overall scale, which must arise from underlying physics such as the seesaw mechanism. We outline how forthcoming precision measurements at JUNO, DUNE, and Hyper-Kamiokande can decisively confirm or falsify this 90° sum rule, offering a minimalist yet testable organizing principle for lepton flavor mixing that bridges data, geometry, and symmetry.