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An Exact Connection between π and the Golden Ratio φ

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  • Luis Teia

Abstract

This article establishes a geometrical and mathematical bridge between the universal constant π and the golden ratio φ by interrelating the construction of the area of a circle using two approaches- one formed using the rotation of a regular unit pentagon and the other one from the rotation of its inverse ― the pentagram of side reference φ . The mathematical end result is a linear expression of π as a function of φ . As an interesting side result, an expression for the area of a circle is derived based on the golden ratio φ and a geometrically motivated coefficient. A scripted program for the verification of the derived expressions is provided.

Suggested Citation

  • Luis Teia, 2022. "An Exact Connection between Ï€ and the Golden Ratio φ," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(3), pages 1-20, June.
    • Handle: RePEc:ibn:jmrjnl:v:14:y:2022:i:3:p:20
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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