Not all constants are empirical. Some constants are mathematical invariants that appearwherever form closes upon itself in a stable way. π appears when rotation closes into circumference. e appears when growth or decaybecomes continuously recursive. φ appears when proportion becomes self-similar. TheFeigenbaum constants appear when recursive bifurcation approaches chaos throughuniversal scaling. These constants are not measured in the same sense as physical constants. They arediscovered through mathematical structure. Yet physics depends on them because physicallaw must become mathematically expressible before it can become experimentallymeasurable. This paper calls such constants mathematical closure constants. A mathematical closure constant answers What invariant form appears when a mathematical operation achieves closure? The central claim is: Transcendental constants are formal invariants of closure, recursion, proportion,and transition. They form part of the grammar through which coherence becomes geometry, growth,proportion, turbulence, bifurcation, and measurable law.
Philip Lilien (Thu,) studied this question.