The Geometric Triangle Decomposition of the Riemann Zeta Function
Abstract
We present a geometric framework connecting the trivial zeros of the Riemann zeta function (s = -2n) with the non-trivial zeros (s = 1/2 + it_n) through right triangles with vertex at the origin. We prove that the first angle θ₀ ≈ 81.95° is the strict global maximum (the "brit milah property"), identify inflection points corresponding to prime number deserts, and reinterpret the classical identity |χ(1/2+it)| = 1 as optical impedance matching at the critical line. 9 pages, 7 figures. Computational collaboration with Claude (Anthropic).
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 February 2026
- Document type
- Preprint