New ideas on geometrical design in Malay mengkuang weaving motifs Mathematical

The art of Malay mengkuang weaving motifs started from 100 years ago in the states of Malaysia particularly in. Thus, due to its past history, there are now 51 types of motifs gathered and more new ideas emerged. A study has been done on 16 motifs produced by the weavers in Bukit Tanah and Kota Bharu, Kelantan and analysis have been made upon the changes of ideas on the above-mentioned motifs. The data collection was through observation and analysis of the mengkuang weaving and also by interviewing the mengkuang weavers. The input obtained was then analyzed to understand the new ideas in Kelantan Geometrical design in mengkuang weaving. Four main areas of kelarai mengkuang were selected in order to analyze the geometrical designs in its essential value, but also for its substantial contribution, for the socio-economic development in the industry. Due to the above-mentioned condition, the main objective of this research is to identify the new ideas on Geometrical Design in Malay mengkuang weaving motifs. The analysis showed that the weavers have applied mathematical thinking in the design of mengkuang weaving. Hence, this research will contribute more information to the body of knowledge in mengkuang weaving and its relation to mathematical tools thus should be preserved for the benefits of the Malaysian heritage.


Introduction
*Weaving is a traditional form of art inherited from our ancestors without any external foreign influences. Weaving involves the process of crisscrossing raw materials obtained from special selected plants to be formed into usable products. There are six types of weaving which are mengkuang leaves, pandan leaves, Wild Bornean Sago leaves, rattan core, coconut leaves and fern leaves weaving. The mengkuang weaving main item for this research, involves the same process of crisscrossing the dried processed mengkuang leaves in making mats and other handicrafts as a leisure time activity that also generates part time income for women in the east coast of Malaysia.
According to DeWalt and DeWalt (2011), the existence of motif of all types of weaving is shaped from the image repetitions and also noted from small designs. The shape is arranged structurally; where it follows the sequence that has been decided until it forms a pattern.
The production of each individual motif is also linked to the arrangement aspect of an object, whereby it involves arranging both organic and geometric shapes. This motif arrangement which has been done in repetitions would naturally involve other elements available in the design element like line, shape, value and color was explained in Ismail (Ismail, 2007). The repetition will also produce a new design called all over pattern.
Furthermore, the inspiration and creativity of the weavers can be seen by adding or subtracting the patterns to become a new pattern. Exposure to shapes also provides experiences that are keys to developing spatial thinking more broadly. This art is considered as a heritage craft that needs to be supported not only for its essential value, but also for its substantial contribution, for the socio-economic development in the industry (Melati, 2010). Due to the above mentioned condition, the main objective of this research is to identify the new ideas on Geometrical Design in Malay mengkuang weaving motifs. Today it is a dire need for the preservation of the cultural heritage of Malaysia to ensure that this valuable asset will be in the heart of every Malaysian.
If you were to picture any type of repeating pattern, you would be able to picturing a pattern that classified one of only 17 district symmetry groups (Nelson et al., 2012). The symmetry group of the patterns includes is all isometries such as translations, rotations, reflections or glide reflection which map the pattern onto itself. However, the most popular representations of these symmetry groups were introduced by a Dutch graphic artist M.C. the tessellation concept. A "periodic pattern" or "repeating pattern" or "kelarai" on the other hand are created to make two-dimensional design to fill the plane are called wallpaper groups. Every periodic pattern or structure associated to it is called a lattice of points. The lattice unit is the set of all images of that when acted on by isometries. There are 5 five types of lattice such as parallelogram, rectangular, rhombic, square and hexagonal. Ismail (1997) stated that motifs are also classified as on theme, while patterns are visual elements arranged in such a manner that they cover the same area as that of motif form. The most appropriate description for pattern is motif arrangement. When motifs are arranged in single unit repeats it can be called as a spot repeats. Motifs that are arranged in rows are called stripe repeats. A motif is something that is related to pattern in design. The different of basic unit will get from the arrangement of the basic unit, cell or original pattern (model) is repeated and it is referred to as a motif (Otto, 2002).

Literature review
According to Ismail (1997) the geometrical shape in weaving is divided to three categories like original geometrical design, natural geometrical design and arrangement of the geometrical design. The original geometrical designs have existed for many years. In these motifs, combination of lines can produce geometrical shapes without a particular shape. The simple shape and in geometrical 'mengkuang' weaving design was first known as 'gadas'. According to Ismail (1997) that is a normal weaving or weaving without motifs. Hajah Rokiah Haji Mahmud stated that the Malays produced weaving products based on natural environment. Such natural characteristics consist of 2 main shapes namely the plant characteristics and animal characteristics. Such characteristics are image stemmed from observation of certain plants and parts of animals, insects and so on and translated into geometrical shape. Some of plant characteristics are tampok jantung motif based on the shape of the center part of a tree or flesh of a young (Serian Motives published by Kraftangan).
The geometrical arrangement design is a combination of natural geometrical design in producing an abstract. Some of the examples of geometrical arrangement design are known as belah ketupat Motif, buntut siput Motif, pucuk rebung Motif, kisar mengiri Motif, sisik kelah Motif (Ismail, 1997). There are changes geometrical design in motif according to time changes. Motif that has been produced is a development of geometrical shape with plus and minus operation shape geometrical for producing new motifs (design). Table 1

Method
In the research objective, it stated the need to identify the new ideas on Kelantan Geometrical Design in Malay mengkuang weaving motifs, hence qualitative study was chosen. We have selected 6 mengkuang weavers in Kota Bharu and Bukit Tanah Pasir Puteh Kelantan. The data collection was through observation and analysis of the mengkuang weaving and also by interviewing the mengkuang weavers. The input obtained was then analysed to understand the new ideas in Kelantan Geometrical design in mengkuang weaving. An analysis of the new ideas on geometrical design in few motifs of mengkuang weaving was made.

Results and discussion
An analysis of the 6 motifs, out of 51 mengkuang weaving motifs was made. The selected motifs were analysed to identify new ideas of the geometrical designs. Interviews with the mengkuang weavers were carried out to gain information about mengkuang motifs. Finally, conclusions were made based on the analysis.
Four main areas of kelarai mengkuang were selected in order to analyse the geometrical designs in mengkuang weaving motifs.

Evolution of Idea on Kelarai Bunga Cempaka to Kelarai Berakar
The Kelarai Bunga Cempaka was found in 1957. The Kelarai Berakar was inspired by the Kelarai Bunga Cempaka because of the similarities in the square shape. Fig. 2 shows Kelarai Bunga Cempaka contains reflections, translations and rotations. The centers of the rotations lie on the reflection axes. The lattice is a square. Fig. 3 shows that Kelarai Berakar contains reflections axes at 90 degree angle, glide-reflection, translations and half-turn rotations. The centers of the rotations lie on the reflection axes. The lattice is a square. The basic design found are Kelarai Bunga Cempaka which was originally emerged from Kelarai Motif Flora. The evolution from these two types of kelarai extremely non-ordinary where ideas could develop despite their motifs. The basic designs could clearly be seen between these two types of kelarai.

Fig. 3: Kelarai Berakar
The basic shape can clearly be seen between the two types of kelarai include the different size of square. Here the square is in the smallest size. Whereas the size of the square on the kelarai Bunga Cempaka is bigger (involves 15x15 total numbers of the boxes) compared to the size of kelarai Berakar which is smaller (involves 11x11 total numbers of boxes). This indicates that 8 rows and 8 columns are deleted to produce kelarai Berakar.
Based on Fig. 4, it is found that these 8 rows and 8 columns are deleted which involve 28 square boxes. This is represented by the yellow boxes. For completing the kelarai 4 units squares boxes are added (red coloured) as shown in Fig. 5.

Evolution of idea on Kelarai Bunga Melur to Kelarai Bunga Cengkih Beranak
The Kelarai Bunga Melur is produced in parallel with the production of Kelarai Bunga Cengkih Beranak. This motive sparks from the combination of Kelarai Bunga Cengkih Beranak and Kelarai Bunga Cengkih. In Fig. 6 below, Kelarai Bunga Melur contains reflections axes at 90 degree angle, glidereflection, translations and half-turn rotations. The centers of the rotations lie on the reflection axes. The lattice is a square. On the other hand, kelarai Bunga Cengkih contains reflections axes at 90 degree angle, glide-reflection, translations and half-turn rotations. The centers of the rotations lie on the reflection axes. The lattice is a square.
The basic shapes that are clearly seen on both kelarai are small size square arrangements which are also arranged to 4 different parts. Each square is arranged from 9 small boxes. In the middle of kelarai Bunga Melur, there is only one box whereas 4 more boxes are added to kelarai Bunga Cengkih.

Fig. 6: Kelarai Bunga Melur and Kelarai Bunga Cengkih
Based on observation, the yellow cubes are deleted. In the center of kelarai are added 3 cubes to produced kelarai Bunga Cengkih as shown in Fig. 7.

The evolution of idea from Kelarai Beremban to Kelarai Bunga Cina
The bunga beremban motif was developed from the bunga cina motif as shown in Fig. 8. Under their creativity, the Kelantan weavers have made an amendment to design a new kelarai by adding a column with 4 cubes or row with 4 cubes on the left and the right side of the polygon. The effect of adding these rows and columns are the size will become bigger from the original size of Kelarai Bunga Bemban. At the centre a cube is added to the left and right to the original cubes and add one layer to the kelarai Bunga Bemban as shown in Fig. 9.  Table 2 shwos the summary of the production of kelarai which apply mathematical instruments.

Evolution of idea on Kelarai Kepala Lalat to Kelarai Mata Ketitir
The Kelarai kepala lalat was produced when Handicraft Development Centre took over.
The original features of kelarai kepala Lalat is square fence (Fig. 10). The kelarai mata ketitir is produced by deleting the third row and fifth row (can be seen in stage 1). Then, move then first row and second row in a downward mode. Finally, move the seventh row and eighth row in an upward mode as shown in Fig. 11.   Table 3 shows the summary of the production of kelarai which apply mathematical instruments.

The evolution of idea from Kelarai Berakar to Kelarai Gelung Paku
The Gelung paku motive is very much identical with Root Motive (Fig. 12) but with different number of boxes whereby a boxes on the left, right, up and down have been deleted. These can be seen in the Fig. 13. Kelarai Berakar is inspired by the roots of plants and trees. The general feature of Kelarai Berakar is the shape of rhombus and square. The rhombus has four sides of the same length with two parallel sides, two opposite interior angles of 90 degree and four symmetrical lines. The square shape has four equal sides. The diagonals are congruent with a perpendicular bisector and have four right angles. Under their creativity the Kelantanese weavers have made an amendment to the design by deleting two squares at the left and the right side of the rhombus.
The effect of deleting these squares are the size will become smaller from the original size of Kelarai Berakar. They name it as Kelarai Gelung Paku because of the size is as small as the head of a nail as shown in Fig. 13.

The evolution of idea from Kelarai Belah Ketupat to Kelarai Berhati
Kelarai Belah Ketupat is a motif based on local delicacy wrapped in woven palas leaves. Kelarai

Kelarai Kepala lalat
Kelarai mata ketitir Stage 1 Stage 2 The outcome Belah Ketupat consists of the arrangement of rhombus that fit perfectly together. The rhombus has four sides of the same length, two parallel sides, two opposite interior angles of 90 degree and four symmetrical lines. The idea that strike into the weavers to meet the demand of their customers are by changing the inside motifs of the rhombus from small rhombus to a polygon. The polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain. The polygon is similar like to the shape of the heart and they named it as Kelarai Berhati. The general feature of Kelarai Berakar is the shape of rows of vertical and horizontal box. In square box a row of horizontal lines is arranged from the top left and right corner. Changes between Kelarai Mok Mek and kelarai sisk kelah are on kelarai sisik kelah without fence in Fig. 14. This includes the square box and the make the kelarai look simpler. Fig. 15 and Fig. 16 show the evolution of kelarai Mak Mek and kelarai Sisik Kelah. Table 4 shows the summary of the production of kelarai which apply mathematical instruments.

Conclusion
New ideas that exist in the mind of the weavers show that they have the knowledge and the intelligence in mathematical thinking and creativity. The development of these kelarai will lead to the heritage.