Rotational symmetry and Scarab seals--论文代写范文精选

在许多宗教符号,对称是用来传达一个直观的意思。我们看到古老的道教形象，有一个有趣的使用对称旋转的中心点,加上黑白反转颜色。实际意义是阴阳的必要性。下面的paper代写范文进行详述。

Abstract 
In many cases, the presence of symmetry in an image turns out to be associated with an idea of beauty, strength and order. Nevertheless, an excessive symmetry can be boring and constraining the creative action. A perfect bilateral symmetry for instance, gives to the observed object a highly static position (an example from an Egyptian bas-relief is shown in Fig.2). In images or statues, a too fixed appearance can be avoided by a slight breaking of symmetry1 . The rotational symmetry is different, because it is quite natural for us to follow the image in its rotation in the space. 

This symmetry produces a feeling of motion and evolution. A breaking of symmetry in this case enhances the idea of inter-penetration or contrast. Let us consider for instance a well-know symbol, the Yin-Yang symbol of Taoism. As in many religious symbols, the symmetry is used to convey an intuitive meaning. And in fact, we see that the ancient Taijitu image of Taoism has a fascinating use of symmetry for rotation about the central point (a two-fold one), combined with black-and-white inversion of colours (see Fig.3). The image actually intends to be a representation of the complementary need for male and female concepts. The rotational symmetry of the shape plus the breaking of colour symmetry, catches our attention with a feeling of development in the frame of complementary actions, not of mere recurrence.

How old is the rotational symmetry in images? Well, we have small objects that can help us in investigating this question, and these artefacts are the stamp seals. In a very old stamp seal from the region North Syria/Iraq/Iran [7], dated 5th-4th millennium BC, we see a standing male figure between two horned quadrupeds back to back and head to end (see Fig.4a). The overall structure of the image is built to respect the two-fold rotational symmetry. On the right side of the same figure (Fig4.b), we see a stamp seal from Susa2 . 

The seal depicts two goatantelopes head to tail, inside and outside an oval [8]. In this seal, the idea of motion is strongly enhanced, the two antelopes seem to run on the rim of the seal. What is the evolution of this kind of images? Let us imagine a breaking of the two-fold rotational symmetry, obtained by depicting two animals again, but in this case a predator/prey couple. The Figure 5 shows a late bronze age seal from Aegeus with a lion and horned quadruped. This is the hunting between two opposite components. And, finally, men fighting with bulls, in a beautiful Minoan stamp (Fig.6). Note the increase in creativity.

To evaluate the presence of two-fold rotational symmetry in images engraved on Egyptian seals, a possibility is to read the catalogues of the huge collections, for instance, of British Museum or Egyptian Museum of Cairo [4-6], when of course, the direct inspection is not possible. The two-fold symmetry seems to be not so frequent among Egyptian scarab seals, depicting animals. In catalogues, we find few scarabs with two symmetric animals (scorpions, lions, crocodiles or lizards, see Fig.7). It is not clear if these seals were unusual or not enough interesting to deserve a place in a museum collection. In fact, the quality of images on these seals is rather poor. In an exiguous number of cases, we observe two different animals. The hunting predator/prey represented in Fig.7 is probably from Hyksos period. The collection of the Egyptian Museum of Torino too has few scarabs with rotational symmetry. We can see a seal with two scorpions and one with two crocodiles. But the collection possesses a quite unusual seal with two men, may be twins (Fig.8). This seal can be dated to 2200-2040 BC, the first intermediate period of Egypt. The former scarabs with human figures were developed during this period. The human figure was depicted with a linear style, as if it were composed by sticks [3].

A huge number of Egyptian scarabs is engraved with coils and spiral, according to the style of the Middle Kingdom. Figure 9 shows a selection of these images from Ref.4. Engraved patterns develop two-fold, four-fold rotational or bilateral symmetries. When we observe these images, we are amazed about the knowledge of plane pattern symmetries of ancient Egyptian and we can ask ourselves how deep was this knowledge. Common opinion is that Egyptians had used all the 17 types of plane patterns. B. Grünbaum discussed the subject in 1984, telling that this is a misconception, because Egyptians appear to have missed the five symmetry groups, which have three-fold rotation [11]. And in fact, on seals we do not observe three-fold symmetric images. To tell the true, it is difficult to arrange such images in an ovoid shape (I found just one attempt, shown in Fig.10, amongst seals in Ref.6).

Conclusions 
This paper discussed the presence of symmetries in images engraved on ancient seals. We can conclude asking ourselves, as P. Gerdes uses in his papers, why symmetry is such a common phenomenon in human culture. An easy answer for the bilateral one seems to be quite naturally associated with the fact that animals and human beings possess this symmetry. But why symmetries, which are rare in nature, for instance the two-fold rotational symmetry, are common amongst us, as noted by Gendes. According to him [12,13], these symmetries can naturally arise in solving problems involved in weaving activities. It is necessary to note that this conclusion is rather specific, because it was reached in studying entanglements of fibres to create baskets or textiles. Nevertheless, we can extrapolate an interesting consequence: the use of symmetries in human artefacts is not a mere copy of natural objects. Symmetries in images started as a creative human action in very ancient times, without the conscious use of geometry.(论文代写)

51Due网站原创范文除特殊说明外一切图文著作权归51Due所有；未经51Due官方授权谢绝任何用途转载或刊发于媒体。如发生侵犯著作权现象，51Due保留一切法律追诉权。(论文代写)
更多paper代写范文欢迎访问我们主页 www.51due.com 当然有paper代写需求可以和我们24小时在线客服 QQ:800020041 联系交流。-X(论文代写)