FIBONACCI SQUARES IN FASHION DESIGN

ARTTE

Applied Researches in Technics, Technologies and Education Journal of the Faculty of Technics and Technologies, Trakia University https://sites.google.com/a/trakia-uni.bg/artte/

ARTTE Vol. 2, No. 2, 2014 ISSN 1314-8788 (print), ISSN 1314-8796 (online), doi: 10.15547/artte.2014.02.002

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FIBONACCI SQUARES IN FASHION DESIGN

Zlatina Kazlacheva

Faculty of Technics and Technologies, Trakia University Graf Ignatiev 38, 8600 Yambol, Bulgaria

mobile: +359889339914, e-mail: [email protected] Abstract: The Golden ratio and Fibonacci sequence are often used in the design for creation of beautiful and harmonic forms. The papers presents design of ladies’ dresses using the both ways of constructing of Fibonacci series tiling with squares. As a result of the use of the both versions of Fibonacci series tiling with squares for designing of aesthetic, beautiful and harmonic clothing, it can be concluded that in fashion design Fibonacci squares can be used in different position, combinations, proportions toward the clothing sizes, and color decisions. Keywords: Fashion Design, Fibonacci Sequence, Fibonacci Series Tiling, Fibonacci Squares.

1. FIBONACCI SERIES TILING WITH SQUARES The Golden ratio and Fibonacci sequence are often used in the design for creation of beautiful and harmonic forms. The Fibonacci numbers are the sequence of numbers { }

defined by the linear recurrence equation

Fn = Fn-1 + Fn-2 (1)

with F1 = F2 = 1. As a result of the definition (1), it is conventional to define F0 = 0. The Fibonacci numbers for n = 1, 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... [2] Fibonacci sequence is used in the creation of geometric objects. There are some versions of Fibonacci series tiling, which are constructed with equilateral geometrical figures – squares or triangles, as the sides’ lengths are equal to the numbers of the Fibonacci series, or the lengths of the sides of the squares or equilateral triangles are each to other in proportions, which are equal to Fibonacci sequence. With the conventional Fibonacci Series, there are two standard ways of constructing the series with interlocking squares. In the version, presented in figure 1, we constantly circle the block to find the next addition site, and end up with a spiral pattern. In the version, which is shown in figure 2, we put two squares side by side, add another square to the longest side, and repeat, darting from left to right as we decide where to put the next square. [1] Figure 3 shows a "quad-spiral" version of Fibonacci tiled squares in the way, which is shown in figure 2. [1] The papers presents design of ladies’ dresses using the both ways of constructing of Fibonacci series tiling with squares.

http://mathworld.wolfram.com/LinearRecurrenceEquation.html

http://mathworld.wolfram.com/LinearRecurrenceEquation.html

http://mathworld.wolfram.com/FibonacciNumber.html#eqn1

http://erkdemon.blogspot.com/search/label/Fibonacci

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Figure 1. Fibonacci series tiling with squares forming a spiral pattern

Figure 2. Fibonacci series tiling with squares which are put side by side

Figure 3. A "quad-spiral" version of Fibonacci tiled squares which are put side by side, shown in figure 2

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2. FIBONACCI SERIES TILING WITH SQUARES IN FASHION DESIGN Figures 4 and 5 present design of ladies’ dresses using Fibonacci series tiling version with squares in a spiral pattern, which is presented in figure 1. In the both dresses the first square of the tiling is situated in center of the waist area. The difference between the model in figure 4 and the one in figure 5 is in proportions of the spiral tiling toward the dress sizes. Analysis of the different color decisions shows that the best way of color combination is that with four colors. Every fourth square is in one and the same color. The 1st, 5th, 9th, … squares are in the first color, the 2nd, 6th, 10th, … squares are in the second color, the 3rd, 7th, 11th, … squares are in the third color, and the 4th, 8th, 12th, … squares are in in the fourth color. In this way the squares, which form a set in one and the same direction, are colored in one and the same color. Figures 6 and 7 present design of ladies’ dresses using Fibonacci series tilling with squares which are put side by side, presented in figure 2. In the both dresses the tiling is situated in the upper part as in the model in figure 6 the first and the second squares are in horizontal direction by the shoulder, and in the dress in figure 7 the first and the second squares are in vertical direction by the shoulder. Other difference between the both models is in the way of constructing color combinations. In the model, presented in figure 6, Fibonacci series tiling are used in bi-colored combination as the odd numbers squares are in one and the same color and the even numbers squares are in another color. In the model, presented in figure 7, Fibonacci series tiling is used is bi-colored combinations too. In this color combination two squares, colored in one and the same color are covered by two squares, which are in another color [1] as the 1st, 4th, 5th, 8th, 9th, … squares are colored in one and the same color, and 2nd, 3rd, 6th, 7th, 10th, 11th, … squares are colored in another color. Figures 8, 9, 10, and 11 present design of ladies’ dresses using the "quad-spiral" version of Fibonacci tiled squares, which are put side by side. The “quad-spiral” version is presented in figure 3, and it is used in the same way in the fourth models of dresses. The centre of the spiral is situated in the centre of the waist area. The used color combinations are the difference between the models. In the model, presented in figure 8, the color combination is constructed in the same way like the model in figure 6 where Fibonacci series tiling are used in bi-colored combination as the odd numbers squares are in one and the same color and the even numbers squares are in another color. In the dress, which is shown in figure 9, the color combination is in the way used in the model in figure 7 where Fibonacci series tiling is used is bi-colored combinations too. In this color combination two squares, colored in one and the same color are covered by two squares, which are in another color as the 1st, 4th, 5th, 8th, 9th, … squares are colored in one and the same color, and 2nd, 3rd, 6th, 7th, 10th, 11th, … squares are colored in another color. The spiral in the model, presented in figure 10 is in three colors combination. The way of combinations of colors uses the sequence, which is uses in dresses, presented in figures 6 and 8. In the model in figure 10, the squares, which form a set in vertical direction up from the waist, are colored in one and the same color. The squares, which form a set in vertical direction down, are colored in the second color, and the squares, which form horizontal sets on the right and on the left, are colored in the third color. The spiral in the model, presented in figure 11 is in four colors combination. The difference with the model, which is shown in figure 10 is that the squares, which form horizontal sets on the right and on the left, are colored in different colors.

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Figures 4 and 5. Design of ladies’ dresses using Fibonacci series tiling with squares forming a spiral pattern

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Figures 6 and 7. Design of ladies’ dresses using Fibonacci series tiling with squares which are put side by side

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Figures 8 and 9. Design of ladies’ dresses using a "quad-spiral" version of Fibonacci tiled squares which are put side by side

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Figures 10 and 11. Design of ladies’ dresses using a "quad-spiral" version of Fibonacci tiled squares which are put side by side

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3. CONCLUSIONS As a result of the use of the both versions of Fibonacci series tiling with squares for designing of aesthetic, beautiful and harmonic clothing, it can be concluded that in fashion design Fibonacci squares can be used in different position, combinations, proportions toward the clothing sizes, and color decisions. Fibonacci squares can be used in fashion design as application, fabrics’ design, pieces of the main clothing parts, etc. The different position, combination, proportions and color combinations of use of Fibonacci series tiling with squares in fashion design according to the body type and size can cover some bodily defects and enhance the beautiful forms. 4. REFERENCES [1] Baird E. (2009). Fibonacci Series Tiling, with Triangles.

http://erkdemon.blogspot.com/2009/06/fibonacci-series-tiling-with-triangles.html. [March-April 2014].

[2] Chandra Pravin and Weisstein Eric W. "Fibonacci Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FibonacciNumber.html. [March-April 2014].

http://mathworld.wolfram.com/topics/Chandra.html

http://mathworld.wolfram.com/about/author.html

http://mathworld.wolfram.com/

http://mathworld.wolfram.com/FibonacciNumber.html

FIBONACCI SQUARES IN FASHION DESIGN

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