Golden Ratio

Authors

  • Dr. Chetansing Rajput M.B.B.S. (Mumbai University) India, Asst. Commissioner (Govt. of Maharashtra)

DOI:

https://doi.org/10.24297/jam.v20i.8945

Keywords:

Pythagoras Theorem, , 3-4-5 Triangle, 1:2:√(5 ) Triangle, Right Triangle, Golden Mean, Divine Proportion, Golden triangle, Golden Ratio and Pi Relationship, Metallic Means, Golden Ratio, Fibonacci sequence, Pi (π), Phi(φ), Pi (π), Phi(φ), Fibonacci sequence, Golden Ratio

Abstract

This paper introduces the unique geometric features of 1:2:  right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2:  triangle, with all its peculiar geometric attributes described herein, turns out to be the real ‘Golden Ratio Triangle’ in every sense of the term. This special right triangle also reveals the fundamental Pi:Phi (π:φ) correlation, in terms of precise geometric ratios, with an extreme level of precision. Further, this 1:2:  triangle is found to have a classical geometric relationship with 3-4-5 Pythagorean triple. The perfect complementary relationship between1:2:  triangle and 3-4-5 triangle not only unveils several new aspects of Golden Ratio, but it also imparts the most accurate π:φ correlation, which is firmly premised upon the classical geometric principles. Moreover, this paper introduces the concept of special right triangles; those provide the generalised geometric substantiation of all Metallic Means.

Downloads

Download data is not yet available.

Downloads

Published

2021-01-17

How to Cite

Rajput, D. C. (2021). Golden Ratio. JOURNAL OF ADVANCES IN MATHEMATICS, 20, 19–42. https://doi.org/10.24297/jam.v20i.8945

Issue

Section

Articles