A Visual Demonstration of the Golden Ratio via a Contraction Map

American Mathematical Monthly 2026

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Authors: Bikash Chakraborty
DOI: 10.1080/00029890.2025.2600905
Cited by: 0

Abstract

We prove that the Cauchy sequence {1,1+1,1+1+1,…} converges to the golden ratio 1+52.We start with an integer k≥2, real numbers m≥1, a∈[0,k). Define f,g,T:[0,∞)→[0,∞) as f(x)=m+ax, g(x)=xk, and T(x...

Fields of Study & Subjects

Mathematical Dynamics and Fractals Advanced Mathematical Theories and Applications Fixed Point Theorems Analysis

Publication details

Journal / source
American Mathematical Monthly
Volume
133
Issue
4
Pages
315–315
Publication date
5 February 2026
Language
EN