THE REPRESENTATION OF THE GOLDEN RATIO BY THE CONTINUED FRACTION Kim, Seung Soo; Ko, Mi Yeon; Lee, Yong Hun;
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.
golden ratio;continued fraction;iterated fixed point theorem;
R. G. Bartle and D. R. Sherbert, Introduction to Real Analysis, 3rd Ed., JOHN WILEY & SON, 2000.
James F. Epperson, An Introduction to Numerical Methods and Analysis, JOHN WILEY & SON, INC 2002.
A. Y. Khinchin, Continued fractions, Dover Publications, inc., 1997.
S. L. Griffing, The Golden Section : An Ancient Egyptian and Grecian Proportion, Xlibris Corporation, 1998.