• Communications of Mathematical Education
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• v.28 no.2
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• pp.281-302
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• 2014

The purpose of this paper is to offer a history of golden ratio, the criterion raised by Markowsky, and misconceptions about golden ratio. Markowsky(1992) insists that the golden ratio does not appear in the great pyramid of Khufu. On the contrary, we claim that there exists the golden ration on it. Elementary and middle school text books, and domestic history books deal with the great pyramid of Khuff and the Parthenon by examples of the golden ratio. Text books make many incorrect statements about golden ratio; so in teaching and learning the golden ratio, we recommend the design-composition of dynamic symmetry, for example, industrial design, aerodynamic, architecture design, and screen design. Finally we discuss the axial age how to affect the school mathematics with respect to the subject of Thales and the golden ratio.

• International Journal of Contents
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• v.6 no.3
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• pp.71-82
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• 2010

The golden ratio is a mysterious number that surprisingly appears in science, physics, mathematics, as well as in nature. The number 1.618 seems to be a universal constant, and crops up whenever the subject is of beauty or elegance. Beautiful flowers and sea shells and also attractive people have a common number and that is 1.618 or $\varphi$ (phi). This paper does a study into the story of phi, and describes how the golden ratio is derived. Artists, architects and designers have employed the ratio into dimensioning their works of art to achieve visual appeal. Examples such as the Greek Parthenon of the Acropolis and paintings such as the Last Supper all use this magic number. An investigation was conducted among 50 people to test if looking at golden proportioning was actually appealing, or if it was just a type among overzealous enthusiasts. The results show that the golden ratio may actually be of some use.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.4
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• pp.83-93
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• 2017

In everyday life, the ratio of credit card aspect ratio is 1: 1.56, and A4 printer paper is 1: 1.414, which is relatively balanced golden ratio. In this paper, we show the Fibonacci Golden ratio as a polynomial based on the golden ratio, which is the most balanced and ideal visible ratio, and show that the application of Euler and symmetric jacket polynomial is related to BPSK and QPSK constellation. As a proof method, we have derived Fibonacci Golden and Galois field element polynomials. Then mathematically, We have newly derived a golden jacket code that can be used to generate an appropriate code with orthogonal properties and can simply be used for inverse calculation. We also obtained a channel capacity according to the channel correlation change using a block jacket matrix in a MIMO mobile communication.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Archives of Plastic Surgery
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• v.33 no.2
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• pp.168-174
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• 2006

For over two thousand years, many artists and scientists have tried to understand or quantify the form of the perfect, ideal, or the most beautiful face both in art and in vivo(life). However, this mathematical relationship has been consistently and repeatedly reported to be present in beautiful things. This particular relationship is referred to as the golden ratio. It is a mathematical ratio of 1.618 : 1 that seems to appear recurrently in beautiful things in nature as well as in other things that are seen as beautiful. Dr. Marquardt made the facial golden mask that contains and includes all of the 1-dimensional and 2-dimensional geometric golden element formed from the golden ratio. The purpose of this study is to evaluate the usefulness of the golden facial mask. In our cases(n=40), the authors applied the facial golden mask to the preoperative and postoperative photographs, and scored each photograph. Compared with the average scores of the facial mask applied photographs and none applied photographs using non-parametric test, statistical significance was not checked (p > 0.05). It means that the facial golden mask can be used for facial analysis. The facial golden mask is easy to apply, cheap and relatively objective. So, the authors introduce the one of useful facial analyses.

• The Journal of Natural Sciences
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• v.13 no.1
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• pp.7-14
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• 2003

The Golden Ratio has played a significant role in many parts of geometry, architecture, music, art, and philosophy. This number has been the subject of numerous experiments in psychology. It also appears in the newer domains of technology and fractals, In this paper, we investigate and analyze the golden ratio which appears in art, music, and architecture.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.939-947
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• 2010

The Golden ratio which was started to be use by Eudoxos, Greek mathematician, is being used as a tool to explain beauty in various fields like architecture, art, society, nature and so on. In addition, people not only use the golden ratio, also use obesity to consider a standard of beauty. This study's subjects are students of H university. We researched their Golden ratios of their whole body, upper body and lower body. Also, to research their obesity levels, we used Obesity degree, Waist-hip ratio and Percent body fat. According to different features of the subjects, we study differences between the golden ratio and obesity and how the golden ratio of body affects obesity.

• Journal of the Korean Society of Clothing and Textiles
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• v.32 no.2
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• pp.167-178
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• 2008

Despite the fact that chogakpos are part of our wonderful Kyubang(the women's quarters in the Chosun Dynasty) culture with their own unique beauty and artistic values, there has been no scientific and objective proof of their aesthetic values. Once they are proved for their beauty through scientific analysis, they will be recognized worldwide along with our unique culture. The methodology included a review of related literature and theses along with magazines, periodicals, and Internet books. The analysis of lines parting, the dimensions of chogakpos were carried out over 108 pieces introduced in Old Pojagis by Heo Dong-hwa. As for line parting, the dimensions of chogakpos were measured to see if the golden and Geumgang ratio could be applied and to discover their unique partition ratio. As a result, there was the presence of the golden ratio applied to them with the golden curves from golden triangles and rectangles also found therein. The Yeoijumunbo confirmed that there was the golden ratio between the radius of a circle and a side of a regular decagon inscribed in the circle. The common line ratio among the squares, isosceles triangles, wanes, and overlapping rectangles was around 1:1.31, which means that there was a unique line ratio in the traditional chogakpos. Furthermore, the ratio of 1:1.31 was close to the Geumgang ratio commonly used in the traditional buildings of Korea.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.103-112
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• 2014

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.

• Korean Journal of Culture and Social Issue
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• v.28 no.4
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• pp.749-772
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• 2022

This study aimed at investigating the validity of WHR (or waist-to-hip ratio) and Golden ratio as standards of physical attractiveness. Each of 60 male and 60 female college students were divided into two groups of 30. Using the 3D game program, each person in one group drew a physically attractive figure of the opposite sex while the other group drew a physically attractive figure of the same sex. Then, WHR and Golden ratio of the figures were measured and compared with the ideal WHR (.7 for women and .9 for men) and Golden ratio 1.618. It was found that WHR and Golden ratio for the physically attractive figures were lower than the ideal standards regardless of the participant's gender. That is, the participants preferred to men and women having curvaceous body shapes with a narrow waist and a wide pelvis. In most cases, Golden ratios measured in many ways were not correspondent to the ideal ratio, 1.618. In regards to BR (or Body Ratio), the legs and waist of the physically attractive figures were shorter relative to the Golden ratio and this was more salient for physically attractive man figures. Regarding the facial ratio measured by FR(or facial ratio) and FR_VP(or facial ratio_vertical point), the faces of figures made by participants, regardless of their sex, were shorter and wider compared to the Golden ratio. Further, the participants preferred baby-faced woman and masculine man figures. Finally, implications of the findings, limitations the of the present study, and the suggestions for future research were discussed.