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.