THE REPRESENTATION OF THE GOLDEN RATIO BY THE CONTINUED FRACTION

- Journal title : Honam Mathematical Journal
- Volume 36, Issue 1, 2014, pp.103-112
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2014.36.1.103

Title & Authors

THE REPRESENTATION OF THE GOLDEN RATIO BY THE CONTINUED FRACTION

Kim, Seung Soo; Ko, Mi Yeon; Lee, Yong Hun;

Kim, Seung Soo; Ko, Mi Yeon; Lee, Yong Hun;

Abstract

There are several theories to say that `Mathematics is beautiful`, but the typical one of them is a theory about the golden ratio. Often the golden ratio apt to be considered only as the geometric shapes or the simple number of ratio used in buildings and arts. However in this paper, we studied to consider the mathematical theories which are contained in their inside. In particular, we investigate the various expressions of the continued fraction which are represented by the golden ratio.

Keywords

golden ratio;continued fraction;iterated fixed point theorem;

Language

English

References

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S. L. Griffing, The Golden Section : An Ancient Egyptian and Grecian Proportion, Xlibris Corporation, 1998.