Geometric Measurement System Based on 21 / 42 Scaling and Circular–Triangular Structures

AuthorMiljko Tijanic AbstractThis work documents a personal geometric measurement system developed and published openly since 2021. The system is based on fixed ratios (notably 21, 42, 10.5, and their subdivisions), circular packing, triangular constructions, and rotational symmetry. The diagrams presented here serve as measurement references rather than symbolic or interpretive illustrations. DescriptionThe uploaded figures present a consistent geometric framework built from: A base unit of 21 cm, extended to 42 cm Repeating circle radii of 10.5 cm and derived values Grid-based constructions for reproducible measurement Triangle–circle relationships used for subdivision and alignment Even/odd rotational symmetry expressed through four opposing orientations The system emphasizes measurability, scale invariance, and repeatability using simple tools (grids, circles, triangles), including demonstrations of how drawing software introduces rounding deviations compared to physical measurement. Several diagrams illustrate: Linear scaling relationships (21 ↔ 42 are 3 - 6) Circular packing and tiling Triangle-circle intersections Rotational symmetry with 4 and 12 elements Practical measurement error introduced by digital rendering tools No claims are made here regarding institutional adoption, endorsement, or external validation. This record exists to timestamp and preserve the work in its original form, exactly as publicly shared by the author. Purpose of PublicationThe purpose of this Zenodo record is: Long-term public archiving Clear authorship attribution Open access for educational review Protection against misrepresentation or loss This publication does not assert priority over unrelated research, nor does it accuse any institution or individual. It simply documents the material as created and released by the author. License[Choose: CC-BY 4.0 or CC-BY-NC 4.0]