THE GOLDEN AND FIBONACCI GEOMETRY IN FASHION AND TEXTILE DESIGN

International Scientific Conference eRA - 10

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The Golden and Fibonacci Geometry in Fashion and Textile Design

Z. Kazlacheva1, J. Ilieva2

1 Faculty of Technics and Technologies of Yambol, Trakia University of Stara Zagora, Yambol, Bulgaria, Mobile: +359 889339914, E-mail: [email protected]

2 Faculty of Technics and Technologies of Yambol, Trakia University of Stara Zagora, Yambol, Bulgaria, Mobile: +359 897512012, E-mail: [email protected]

Abstract

The proportions of the Golden ratio and Fibonacci sequence associate harmony and beauty and by this reason they are used in design. The paper presents the use of geometrical forms and tilings, created on the base the Golden ratio and Fibonacci numbers, in fashion and textile design. The forms and tilings are the Golden and Fibonacci spirals, the Golden and Fibonacci series tiling with squares, the Golden tiling with triangles, Fibonacci tiling with triangles – Fibonacci Rose, etc. For creation of successful aesthetic fashion and textile design projects these kinds of forms can be used in different combinations and color decisions.

1. Introduction

As symbols of beauty and harmony the proportions in the Golden ratio and Fibonacci are used in creation of different type of forms and tiling, which are used in design. The paper presents the use of geometrical forms and tilings, created on the base the Golden ratio and Fibonacci series, in fashion and textile design. The forms and tilings are the Golden rectangle and triangle, the Golden and Fibonacci spirals, the Golden and Fibonacci series tiling with squares, the Golden tiling with triangles, Fibonacci tiling with triangles – Fibonacci Rose, etc.

2. The Golden and Fibonacci Geometry in Fashion and Textile Design

Figure 1 presents a model of a dress [1] with the spiral form squares tiling on the base of the Golden ratio [2, 3]. A Golden rectangle (a rectangle with proportion of the sides equal to the Golden ratio) is drawn. A square with sides, equal to the larger side of the Golden rectangle, is set on the larger side of the Golden rectangle. Both the Golden rectangle and the square form a bigger Golden rectangle. A square with sides, equal to the larger side of the bigger Golden rectangle, is put to the larger side of the bigger Golden rectangle. The same drawings repeat in the spiral direction and the squares in proportions of Golden ration form a squares tiling in spiral form. This tiling is the frame for creation of the Golden spiral [3]. Figure 2 shows a model of a dress [1] with the use of the side by side squares tiling on the base of the Golden Ratio, which is similar to Fibonacci series squares tiling, created side by side in two perpendicular linear directions, which is presented in [4]. A


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Golden rectangle is drawn. A square with sides, equal to the larger side of the Golden rectangle, is set on the larger side of the Golden rectangle. Both the Golden rectangle and the square form a bigger Golden rectangle. A square with sides, equal to the larger side of the bigger Golden rectangle, is put to the larger side of the bigger Golden rectangle. The same drawings repeat in two perpendicular linear directions and form other variant of squares tiling in side by side or a diagonal form. Figure 3 presents a dress [5] with the side by side squares tiling on the base Fibonacci series [3]. The way of the tiling constructing is the same like the creation of the tiling on the base the Golden section, which is used in the dress, shown in Figure 2. Figure 4 shows a dress with the square tiling in spiral form on the base Fibonacci sequence [4]. The model of the tiling is the same like the construction of the Golden tiling with squares in spiral form, which is used in the dress in Figure 1. The both types of spiral tiling with squares are the bases for creation of the both spirals – the Golden and Fibonacci spirals. The model of the dress in Figure 4 is with design with Fibonacci spiral. In the fashion design the Golden and Fibonacci spirals can be used with or without the frames of the square tilings. Figure 5 presents a design of a dress with the use of the tiling with Golden triangles (isosceles triangles with sides in proportions of the Golden ratio) [6]. The model of tiling is similar like the square tilings in spiral form from Figures 1 and 4, and the spiral tiling with Golden triangles can be a base for a spiral too. Figure 6 shows a model of a dress [7] with design using the tiling with equilateral triangles on the base proportions of the Fibonacci series. This tiling version is named Fibonacci rose [4]. The Fibonacci rose forms two spiral forms, which are the base for double spiral. Figures 7 and 8 present textile designs [8] on the base Fibonacci rose [4]. The design in Figure 8 Fibonacci rose is used as a frame of entered circles. Figures 9 and 10 present textile designs with the use of the square pursuit [9] which forms four Golden spirals. This creation is known as the bugs’ problem too: “Four bugs are standing at the four corners of a square. They are hungry (or lonely) and at the same moment they each see the bug at the next corner over and start crawling toward it. What happens? As they crawl towards each other they spiral into the center, always forming an ever smaller square, turning around and around forever. Yet they reach each other! This is not a paradox because the length of this spiral is finite. They trace out the same equiangular spiral. [10]” Figure 11 presents a textile design with the use of the Golden spiral [3] without the frame of the Golden spiral form squares tiling [2, 3]. Figures 12 and 13 show textile designs with the use of the Golden spiral in the frame of the Golden squares tiling in spiral form and isosceles right-angled triangles, which are entered in the flame of the spiral tiling [2, 3].


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Figure 1: Design of a lady’s dress using the

Golden squares tiling in spiral form. Figure 2: Design of a lady’s dress using the

Golden squares tiling in two perpendicular linear directions.


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Figure 3: Design of a lady’s dress using Fibonacci

squares tiling in two perpendicular linear directions.

Figure 4: Design of a lady’s dress using Fibonacci squares tiling in spiral form and Fibonacci spiral.


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Figure 5: Design of a lady’s dress using the Golden triangle tiling in two perpendicular linear

directions.

Figure 6: Design of a lady’s dress using Fibonacci triangle tiling – Fibonacci rose.


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Figures 7 and 8: Textile designs using Fibonacci triangle tiling – Fibonacci rose without and with entered

circles.


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Figures 9 and 10: Textile designs using the square pursuit which forms four Golden spirals.


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Figure 11: A textile design using the Golden spirals without the frame of the Golden spiral square tiling.


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Figures 12 and 13: Textile designs using the Golden spirals with the frame of the Golden spiral square tiling

and entered isosceles right-angled triangles in the frame of the tiling.


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3. Conclusion

For the creation of beautiful and harmonic fashion and textile designs:

The forms and tiling which are made with the help of the Golden ratio and Fibonacci sequence proportions can be used in combinations on the base one or two types of symmetries: mirror (Figures 9, 10 and 11), radial (Figures 2, 3, 4, 7, 8, 11, 13), and translation (Figures 9, 10, 11, 12) ones. The used Golden and Fibonacci tilings are created on the base spiral symmetry (Figures 1, 4, 5, 6, 7, 8, 11, 12, 13) and translation (Figures 2, 3) and that reflect in the choice of the type of the symmetry in creation of the fashion and textile designs.

The tilings are used as frames for entered elements and these elements can forms designs with or without the tiling frames.

Successful creative process is possible if suitable color schemes are selected. Presented fashion and textile designs are based on 2, 3, and 4 color combinations, which reflect the fashion trends and connections between lines, forms and colors on the base their associations.

Acknowledgements

The work is supported by the scientific project 3.FTT/ 2014 of Trakia University and the Fund of the National budget for scientific researchs in higher education in Bulgaria.

References

[1] Z. Kazlacheva, “The Golden Squares in Fashion Design”, EMIT Economics Management Information Technology, vol. 4, no. 1, pp. 32-38, June 2015.

[2] “Golden Rectangles”, Harvard Mathematics Department Home page, 2000-2014, http://www.math.harvard.edu/archive/101_spring_00/www/gallery/gold/ index.html.

[3] J. Lee, “Logarithmic Spiral”, 10 Lessons in Fractals, Complex Patterns, and Chaos. 2003, http://mathforum.org/lisab/fourth_lesson/part_4.htm.

[4] E. Baird, “Fibonacci Series Tiling, with Triangles”, ErkDemon, 2009, http://erkdemon.blogspot.com/2009/06/fibonacci-series-tiling-with-triangles.html.

[5] Z. Kazlacheva, “Fibonacci Squares in Fashion Design”, ARTTE Applied Researches in Technics, Technologies and Education, vol. 2, no. 2, pp. 91-98, 2014, https://sites.google.com/a/trakia-uni.bg/artte/articles/artte-vol-2-no-2.

[6] B. Clair. “Golden Triangle Spiral”, Math and the Art of MC Escher, 2008, http://euler.slu.edu/escher/index.php?title=File:Golden-triangle-spiral.svg&limit=20.

[7] Z. Kazlacheva, “Fibonacci Rose in Fashion Design”, ARTTE Applied Researches in Technics, Technologies and Education, vol. 2, no. 3, pp. 224-230, 2014, https://sites.google.com/a/trakia-uni.bg/artte/articles/artte-vol-2-no-3.

[8] J. Ilieva, “Fibonacci Rose in Textile Design”, ARTTE Applied Researches in Technics, Technologies and Education, vol. 2, no. 4, pp. 258-269, 2014, https://sites.google.com/a/trakia-uni.bg/artte/articles/artte-vol-2-no-4.

[9] J. Sharp, In pursuit of pursuit curves, ISAMA 99, N. Friedman and J. Barrallo, eds. University of the Basque Country. 1999.

[10] D. Reich, “The Fibonacci Sequence, Spirals and the Golden Mean”, https://math.temple.edu/~reich/Fib/fibo.html.

http://www.math.harvard.edu/archive/101_spring_00/www/gallery/gold/

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THE GOLDEN AND FIBONACCI GEOMETRY IN FASHION AND TEXTILE DESIGN