Simple formulas of \pi\ in terms of \phi
General Mathematics
2024-04-12 v2
Abstract
A re-calculation of a known family of formulas of PI is carried out, revisiting the old Archimedes' algorithm. This allows to identify a general family equation and three new simple formulas of Pi in terms of the golden ratio PHI in the form of infinite nested square roots, with some geometrical properties that enhance the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon's squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio PHI.
Keywords
Cite
@article{arxiv.2403.19684,
title = {Simple formulas of \pi\ in terms of \phi},
author = {Angelo Pignatelli},
journal= {arXiv preprint arXiv:2403.19684},
year = {2024}
}
Comments
10 pages, 5 figures - review process for publishing in JAMP Journal of Applied Mathematics and Physics