2. Golden ratio

Golden Ratio has many perspectives: geometrically, mathematically, and arithmetically. A full understanding of all perspectives as well as the origin of the term is essential, in order to grasp the magnitude from the microscale to the macroscale. In this section, Golden Ratio will be explained term and perspective wise.

The origin of the term Golden Ratio was termed by Phidias. Phidias is a Greek painter, sculptor, and architect. Phidias sculpted the famous Zeus at temple of Olympia, which was considered one of the Seven Wonders of the World. The golden ratio was termed mean of Phidias [6, 8, 15]. There are many terms that reflect the term Golden Ratio: golden mean [2, 7, 10] and extreme/ mean ratio, (Euclid) medial section [3], divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, [11] golden number [6, 15, 8]. In current history, Golden Ratio was termed as Golden Section (goldene Schnitt) by a German mathematician named Martin Ohm who lived from 1792 till 1872. Mark Barr coined the term (phi) to reflect the idea of Golden ratio, in commemoration of Phidias, because many historians [7, 13] claim that Phidias used the Golden Ratio in his sculptures.

Simply, Golden Ratio is a proportion of two unequal segments: the proportion of the long segment to the short segment is equal to the total of the two segments to the long segment, both equal 1:1.61803398874989. In Figure 1, the longer segment a and the short segment b, whereby the proportion of a:b is equal to the total of a and b to a. The number 1.61803398874989 is the value of phi. In this context, the ensuing question is how to derive b from a while keeping the Golden Proportion, phi?

To derive the b segment from the a segment, the following must be conducted: First, draw a square with length a, as articulated in Figure 2, and construct a unit square. Then, at midpoint on the side of the square, draw a line to the opposite side. Next, connect the midpoint to an opposite corner. When using that line as the radius to draw an arc, accordingly, the long dimension of the rectangle is defined.

The simpler picture is reflected in Figure 3 where the "a" and the "b" are shown and the both hold the value of phi, the Golden proportion.

Concluding the section where the origin of the term Golden Ratio was not only clarified but thorough explanation of the geometrical aspect of the ratio was also put forward, in order to comprehend the magnitude of this proportion.

Figure 1. The Golden Ratio represented in line segments [3, 4].

Figure 2. Construction of a golden rectangle.

Vincicirca both based on the golden proportion notion. First, the research gives an introduction about golden proportion known also as golden section. Then, in the second section, the research explains the three dimensions of golden proportion: mathematically, geometrically, and arithmetically. The third section of the research presents the work of FIBONACCI and his series in the golden proportion. Followed by a discussion of the geometry of Golden ratio and the essential proportions in Vitruvian Man, in the fourth section, where 15 essential proportions are explained based on the Vitruvian Man. In fifth section, BAUENTWURFSLEHRE by ERNST NEUFERT [20] is further explained with circle geometry and 29 golden proportions are reflected in the work. In the sixth section, the face and hand proportions in relation to the golden proportion are further explained. Based on the findings of the previous sections, the seventh section suggests two algorithms to be used when building a human body model. Thereby, presenting more than 35 proportions and measurements used to model human body model along with a simple algorithm that calculates exact measurements. As such, the research facilitates and explains for the human modeler the process of human modeling in multimedia arena. Hence, this research will be a spring board for researchers, practitioners in human

Dubbed by the Greeks, "Golden Ratio" is a mathematical relation and proportion, where the length to width of a rectangle proportion is 1:1.61803398874989484820, such proportion is most suited for human eye and is used by architects, artists, sculptures in their work. While the Golden Ration does not embody every structure or pattern in the universe, yet, historically, this ratio emerged in Great Pyramid of Giza/Khufu/Cheops (2560 BC) [21], and in Vitruvian Man by Leonardo da Vinci and Neufert. More notably, in today's multimedia, Golden Ratio is used in many applications: plastic surgery simulation software, animation software, art, architecture, sculpture, anatomy. A close exploration of such divine proportion and the related applications, offers opportunities to connect an understanding the conceptions of ratio and proportion to the geometry, proportions, and ratio related to the Vitruvian Man and its relation to Bauentwurfslehre by Ernst Neufert (1936) [20]. Throughout the next sections, a detailed explanation will be given to golden ratio: geometrically, mathematically, and arithmetically.

Golden Ratio has many perspectives: geometrically, mathematically, and arithmetically. A full understanding of all perspectives as well as the origin of the term is essential, in order to grasp the magnitude from the microscale to the macroscale. In this section, Golden Ratio will be

The origin of the term Golden Ratio was termed by Phidias. Phidias is a Greek painter, sculptor, and architect. Phidias sculpted the famous Zeus at temple of Olympia, which was considered one of the Seven Wonders of the World. The golden ratio was termed mean of Phidias [6, 8, 15]. There are many terms that reflect the term Golden Ratio: golden mean [2, 7, 10] and extreme/ mean ratio, (Euclid) medial section [3], divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, [11] golden number [6, 15, 8]. In current history, Golden Ratio was termed as

modeling in multimedia field.

114 Machine Learning and Biometrics

2. Golden ratio

explained term and perspective wise.

Figure 3. A golden rectangle with longer side a and shorter segment b.
