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

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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.

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