Asha Materia: Harmonic Membrane Dynamics and the π-Seam Field

When the traditional circle is unfolded into a right triangle, its base-to-radius ratio produces a slope of 17.6568°, derived directly from π. Asha Logic introduces a minute 0.11° seam that reframes this geometry without breaking it, yielding a 17.7668° slope — a difference that defines the harmonic structure of the 22.5° circle. This paper provides the foundational geometric and trigonometric derivation supporting all Asha π-Seam–based models, serving as the mathematical appendix for the Asha Research Series.