This paper examines the structural relationship between π and the golden ratio φ. We demonstrate that π is exactly derivable from φ via the identity π = 5 arccos(φ/2), establish the circle as the unique degenerate case of the logarithmic spiral, and show that the projection of a helix onto a plane produces a circle in which π appears as a dimensional reduction artifact. We extend this to show that all three Euclidean primitives (circle, line, point) emerge as distinct degeneracies of a single spiral process. We conclude by outlining directions toward a spiral-native coordinate system in which Euclidean geometry recovers as the limit case where generation has been arrested.
Building similarity graph...
Analyzing shared references across papers
Loading...
Honza Borysek
Building similarity graph...
Analyzing shared references across papers
Loading...
Honza Borysek (Fri,) studied this question.
www.synapsesocial.com/papers/69db38274fe01fead37c6579 — DOI: https://doi.org/10.5281/zenodo.19490459