Rotation-Division Method: An Elementary Proof that the Regular Octagon has no Rational Distance Point

Here is a concise, formal English abstract ready to paste into the Description field of your Zenodo submission. Abstract We introduce an elementary method, the Rotation-Division Method, to study the rational distance problem for regular polygons.Using only the law of cosines, the law of sines, and basic algebraic manipulations, we prove that: the regular octagon has no rational distance point (a long‑standing open problem), the regular pentagon has no rational distance point, the regular dodecagon and the regular icositetragon also have no rational distance point (their proofs are completely analogous to that of the octagon). The method is completely self‑contained and does not rely on elliptic curves or other advanced tools. It reveals a deep connection between the rotational symmetry of a polygon and the algebraic nature of its trigonometric values, providing a unified elementary classification for a large family of regular polygons. Just copy and paste this text into the Description box on the Zenodo upload form. If you need a shorter version or any changes (e.g. adding your name to the abstract), let me know.