The Numerical Revolution: How the Omega Constant Eliminates Degrees and Transforms Geometry

This paper presents the definitive case for eliminating angular degrees in geometric theory and practice. By applying the Omega constant (Ω = π / log(13) = 52378158 / 42764081), Eric Needham demonstrates that geometric measurement can be conducted entirely through direct numerical relationships based on area, rather than arbitrary angular divisions. Building on earlier work that linked equilateral triangle and circle areas through Ω, this paper expands the framework to include squares, right triangles (via a novel reframing of the Pythagorean theorem), and implications for dimensional analysis. It explores how Omega-based calculations outperform traditional angular computations in CAD and engineering, and proposes a restructured mathematical hierarchy where angles are derived rather than foundational. The work concludes by highlighting implications for mathematics education, physics (wave mechanics, quantum theory), and engineering, initiating a full transition from arbitrary units to absolute numeric truth. License: Creative Commons Attribution 4.0 NC - ND BY 4.0)Author: Eric NeedhamDate: May 17, 2025