The 120° Constant: A Geometric Law of Closure for Triadic Systems

This record contains the paper: The 120° Constant: A Geometric Law of Closure for Triadic Systems The paper presents a formal geometric result concerning the placement of a junction connecting three fixed anchors under equal tension in a Euclidean plane. It establishes the necessary and sufficient conditions under which a unique interior minimiser of total connection length exists and shows that, when such a minimiser is admissible, the three connecting segments meet pairwise at angles of exactly 120°. The result is equivalent to the classical Fermat–Torricelli (Steiner) point for three terminals with equal weights. The contribution of this work lies not in the discovery of that point itself, but in its formulation as a law of closure: a clean, operational statement with explicit admissibility criteria, computational procedures, and clearly defined limits of validity. The analysis is strictly bounded to static, planar (Euclidean) geometry with three fixed, non-collinear anchors and equal scalar tension along straight-line connections. No claims are made beyond this scope. Dynamic systems, non-Euclidean metrics, oscillatory phenomena, biological or psychological interpretations, and unequal-tension cases are explicitly excluded, except where briefly noted for completeness. This record is intended as a stable, citable archive contribution for researchers working in geometry, optimisation, network design, and related applied fields. Related Materials & Extended Context The following resources provide supplementary context, development history, and adjacent research. They are not required to understand or apply the framework presented in this record. Zenodo Archive — Crippin’s Theory (Finalised Volumes)https://zenodo.org/communities/atlas-codex/ NotebookLM Research Series(Developmental analysis and source synthesis)https://notebooklm.google.com/notebook/911b50f2-19a3-487d-9141-512437a668b6https://notebooklm.google.com/notebook/098f3f2a-706b-4e8d-8037-a29d7b3236aa PhilPapers Index Entryhttps://philpapers.org/rec/CRITAW Google Scholar Index (related works)https://scholar.google.com/scholar?q=Crippins+Theory Contact & Access Author: Suzanne CrippinEmail: suzannecrippin@icloud.comLinkedIn: https://www.linkedin.com/in/atlascodex