The Pythagorean Constraint on the Nontrivial Zeros of the Riemann Zeta Function

We propose a novel geometric-functional hypothesis explaining why the nontrivial zeros
of the Riemann zeta function must lie on the critical line ℜ(s) = 1/2. By interpreting the
complex argument as a vector and analyzing the constraints imposed by the Pythagorean
theorem, we suggest that only σ = 1/2 yields a balance enabling the zeta function to reach
zero. The approach is complemented by numerical illustrations and several related
geometric conjectures.