NEW DISCOVERY (Today, June 28): The Hexagonal Logarithmic Spiral (Log Base 1.1547 derived from the ratio of the Hexagon's inherent Right Triangle's Hypotenuse/Height: 4/3^1/2 and (2)/(3^1/2)) in Mod 12 is the Geometric basis of the Whirlpool Galaxy (M51), NOT the Natural Logarithm (Euler 2.7182818).
The pitch of this particular Galactic Spiral has been the subject of much academic research as this was the first of several "Spiral" galaxies thus identified. Until now, this Galaxy had been identified using the Natural Logarithm (Euler) with an 'awkward' pitch adjustment (swipe right for photos demonstrating the obvious departures (in spirality/pitch) from the Natural Log (e) for both this Galaxy and a Nautilus, which geometric basis is the Octagonal Log Spiral (Mod16), see prior post); a pitch adjustment variance from the Natural Log is strange because it negates the Natural Log as its geometric basis!).
The simplicity of this newly discovered Geometric approach (based upon simple Polygonal Geometry found literally everywhere in nature) allows us to see, for the first time, the Scalar structure (Right Triangles, perhaps pointing us toward a demonstrable relationship to gravitational waves?) that underlies the Whirlpool Galaxy's inherent architecture. Based on these findings, my research team will likely publish these results (along with several other known Spiral 🌀 Galaxy structures) as the Mathematical proof (for a Physics publication) is both straight forward and self-evident, with the RIGHT TRIANGLE as the Geometric Convergence Principle.