Acrolysis The Geometric Inevitability of φ–π–e Unity

This paper introduces Acrolysis, a previously unrecognized geometric configuration formed by the three fundamental transcendental constants φ\varphiφ (golden ratio), π\piπ, and eee. We prove that these constants form a unique triangle whose circumradius equals exactly π/2\pi/2π/2, establishing a precise geometric synthesis of optimization, periodicity, and exponential dynamics. The triangle exhibits a distinctive dual symmetry, simultaneously approximating equilateral (60°) and right-angled (90°) geometries. We further extend this structure into three dimensions, defining the Trinity Tetrahedron, whose volume converges to the golden ratio when the apex height is constrained by the exponential constant eee. All claims are supported by explicit analytical derivations and a complete high-precision computational verification script included in the appendix. Acrolysis is presented not as numerical coincidence but as a geometric inevitability: any system requiring optimization, curvature, and exponential evolution must manifest this configuration. The results provide a unifying geometric foundation linking transcendental constants across mathematics, physics, and complex systems theory. of physical reality. For further information please contact, Eric Needham:ensotheory1@gmail.com