What question did this study set out to answer?

The aim is to derive a new geometric ratio cπ that parallels the classical π in Euclidean geometry.

April 13, 2026Open Access

A Geometric Ratio cπ Derived from the Spacetime and Speed of Light geometry

Key Points

The aim is to derive a new geometric ratio cπ that parallels the classical π in Euclidean geometry.
Derived cπ using axiomatic principles from PA and geometric constructs.
Identified cπ in the context of hydrogen atom characteristics.
Examined the relationship between cπ, speed of light, and spacetime geometry.
cπ calculated as 1.7734573703×10^-28, representing a new ratio in spacetime.
Found cπ has a concrete relation to electromagnetic dimensions in the hydrogen atom.
Demonstrated that light traverses a certain distance in Planck times, showing a unique relationship with c.

Abstract

The central new result of this version is the geometric ratio cπ = α^ (61/10) / (4π A (4) ⁵) =1. 7734573703×10^-28 — the spacetime analogue of π, derived entirely from PA axioms. Justas π is forced by Euclidean circle geometry, cπ is forced by the 1+3 spacetime ℍ geometry andthe ℂ/ℍ Hurwitz boundary. It is identified concretely in the hydrogen atom as the ratio α/ (2π × d), where d is the diameter between the two antipodal electromagnetic vertices. The photoncrosses that diameter in exactly d Planck times at speed exactly 1. cπ is the completegeometric characterization of c. The value 299, 792, 458 m/s is its shadow in human units.

A Geometric Ratio cπ Derived from the Spacetime and Speed of Light geometry

Key Points

Abstract

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