The Abstraction Gap Between Mathematics and Physics: The Hidden Compromise in Dimensional Analysis Resolved

In this dataset we bridge the abstraction gap between mathematics and physics by adopting a geometric perspective of trigonometry. We formalize this by addressing the arc length of a circular sector and defining the circular functions axiomatically as direct functional mappings from the physical parameters of a circular sector – namely the radius and the arc length – to its orthogonal projections. Finally, we demonstrate the utility of this framework by modeling simple harmonic motion and uniform circular motion through these geometric functions.