Version 1
: Received: 29 December 2023 / Approved: 29 December 2023 / Online: 29 December 2023 (14:40:21 CET)
Version 2
: Received: 2 January 2024 / Approved: 4 January 2024 / Online: 4 January 2024 (07:24:36 CET)
How to cite:
Pan, H. Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral. Preprints2023, 2023122321. https://doi.org/10.20944/preprints202312.2321.v1
Pan, H. Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral. Preprints 2023, 2023122321. https://doi.org/10.20944/preprints202312.2321.v1
Pan, H. Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral. Preprints2023, 2023122321. https://doi.org/10.20944/preprints202312.2321.v1
APA Style
Pan, H. (2023). Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral. Preprints. https://doi.org/10.20944/preprints202312.2321.v1
Chicago/Turabian Style
Pan, H. 2023 "Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral" Preprints. https://doi.org/10.20944/preprints202312.2321.v1
Abstract
This paper serves as a seamless continuation of the previous work titled "Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers." Upon revisiting the data, a noteworthy observation emerged: the special spirals can be meticulously aligned with the prime spiral on a point-by-point basis through careful scaling and rotation for the parameter ρ remaining a constant greater than one. As ρ increases, both the scaling factor and rotation angle exhibit a corresponding augmentation, albeit with an intriguing caveat—the rotation angle asymptotically approaches its limit of 90°. Notably, the galactic spiral can be perceived as a remarkably close approximation of the Archimedean spiral, with the degree of proximity increasing as ρ grows larger. Furthermore, an intriguing correspondence arises when ρ takes on a value of 1; at this value, the galactic spiral bears a striking resemblance to the Fermat spiral, the space between two consecutive spiral loops undergoes a continuous reduction as the loop's radius expands, yet it never diminishes to zero; simultaneously, the area between two successive loops experiences an augmentation with the value of ρ.
Keywords
Galactic spiral; Prime spiral; ROTASE model; X-matter.
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
