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.v2
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.v2
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.v2
APA Style
Pan, H. (2024). Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral. Preprints. https://doi.org/10.20944/preprints202312.2321.v2
Chicago/Turabian Style
Pan, H. 2024 "Galactic Spiral from ROTASE Model with Large Enough ρ Is Equivalent to Archimedean Spiral" Preprints. https://doi.org/10.20944/preprints202312.2321.v2
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.
Received:
4 January 2024
Commenter:
Hongjun Pan
Commenter's Conflict of Interests:
Author
Comment:
The equation (2) has critical typing error and has to be revised. In the Verion 1, the dx = Vr * sin(α) *dt, dy = (Ve - Vr*cos(α) * dt, one close bracket ")" is missing in the dy equation. However, the correct formulas should be dx = Vr * cos(α) *dt, dy = (Ve - Vr*sin(α)) * dt. The error has been corrected in this new version.
Commenter: Hongjun Pan
Commenter's Conflict of Interests: Author