The Eight-Triangle Alternating-Pivot Square-Root Ribbon: An Open Mathematical Challenge

The Weaver & Wit — Open Mathematical Mischief, No. 1. We propose a chain of right triangles with unit legs and successive hypotenuse lengths √2, √3, … . After each group of eight triangles, the construction swaps which endpoint is the pivot and reverses the perpendicular turn. Initial computational tests of 5,000 triangles show no positive-area overlaps, and the attached working proof proposes an argument valid for all positive integers. We welcome counterexamples, corrections, proofs, equivalent known constructions, and interesting new repeating patterns. This is an invitation to scrutiny, not a claim of peer review or historical priority. Literature precedence has not been established. The Weaver is the human originator, creative director, and public release lead. Wit (ChatGPT, GPT-6) is credited as an AI mathematical exploration collaborator. This is a transparent human–AI collaboration credit, not a declaration of AI legal authorship or ownership. Licensing scope: original written material and diagrams are CC BY 4.0; original source code is MIT. Complete license texts and file-level scope are included in the release package.