Smartex 2015

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0-ABSTRACTS BOOK_

1-COMPRESSION ABILITY OF KNITTED MATERIALS FOR UNDERWEAR _

2-FABRIC ENGINEERING: A SCIENTIFIC APPROACH AND ANALYSIS

3-IMPROVEMENT OF SOIL RELEASE FROM COTTON FABRIC WITH LOWPRESSURE PLASMATREATMENT

4-SCIENCE WITHOUT TECHNOLOGY: ANCIENT EGYPTIAN TEXTILES'

DYEING APPLIED ON SELECTED EXAMPLES AT AZHAR MUSEUM

5-DISCHARGE PRINTING PROCESS OF DYED POLYAMIDE KNITTED FABRIC

6-MECHANICAL & FUNCTIONAL CHARACTERIZATION OF UNCONVENTAIL KNITTED FABRICS

7- ON THE QUESTION OF ENVIRONMENTALLY SENSITIVE UPHOLSTERY MECHANICALPROPERTIES ON THE BASIS OF WARP KNITTING FABRICS

8- IMPACT OF SPRING ULTRAVIOLET RADIATION ON COLOR VALUE AND BURSTING STRENGTHOF THE KNITTED FABRICS

9- NEW APPROACH FOR PHYSICAL ASSESSMENT OF LIGHT FASTNESS OF DYING WOOL YARNS

10-THREE-DIMENSIONAL OF CRINKLES _ElSayed ElNashar_ Aleksandr Smirnov

11- Pressure produced by single and multilayer elastic textile in the therapeutic treatment of venous leg ulcers

12-ERGONOMICS DESIGN OF THE SEWING OPERATOR WORKPLACE

13- DEFECT DETECTION in GARMENT INDUSTRY by ANN

14- POROSITY AS A KEY PARAMETER OF FABRIC PERFORMANCE

15-INFLUENCE OF INDUSTRIAL WASHING ON DENIM FABRICS PROPERTIES

16-E-GARMENT ELEMENT INCLUDING RADIOFREQUENCY IDENTIFICATION SYSTEM

17-USING OF BIOGEOMETRY ENGINEERING TO OBTAIN ADVANCED

WOVEN DESIGNSFOR THE TREATMENT OF DEPRESSED CHILDREN

18- ACOUSTIC STUDY OF INSULATORS MANUFACTURED FROM TEXTILE WASTE: THE CASE OFTHE LINTERS STRUCTURE

19- DEVELOP A MODEL TO IDENTIFY AND CONTROL THE RELIABILITY OF PIPELINES

20- RESEARCH WEFT INSERTION MECHANISM OF THE RIBBON WEAVING MACHINE FORDEVELOPMENT OF TAPES OF TECHNICAL PURPOSE

21- QUALITY MANAGEMENT FOR STUDY COMPUTER SENSOR NETWORKS

22- APPLICATION OF COMPUTER VISION TECHNIQUES IN ASSESSING THE SLAUGHTERINDICATORS OF CROSSBRED LAMBS

23- THE DEVELOPMENT OF DATABASE FOR COMPUTERIZED DESIGNING “THE ARMHOLE-SLEEVE” SYSTEM FOR A RANGE OF BODY SIZES

24-Enhancement of the aesthetics appearance and softness of knitted spacer fabric

25- LOW-WASTE AND RESOURCE-SAVING TECHNOLOGIES TO PRODUCE MEDICAL GAUZEFROM COTTON MIXES WITH ADDED TEXTILE WASTES

26- LOW-WASTE AND RESOURCE-SAVING TECHNOLOGIES TO PRODUCE MEDICAL GAUZEFROM COTTON MIXES WITH ADDED TEXTILE WASTES

27- THE GOLDEN AND FIBONACCI SPIRAL TILINGS IN FASHION DESIGN

28- THE GOLDEN SPIRAL IN TEXTILE DESIGN

29- FASHION DESIGN OF LADIES’ DRESSES IN CLOSE FITTED SILHOUETTE

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5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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THE GOLDEN SPIRAL IN TEXTILE DESIGN

Julieta ILIEVA Abstract: The geometrical forms which are based on the proportion of the Golden ratio are harmonic shapes and they are used in textile and fashion design. The paper presents the use of the Golden spiral in textile design. Essentially the golden spiral is spiral symmetry or it forms spiral symmetry and for creation of beautiful and harmonic forms in the textile design it is used in combination which are based on the rhythms, results of the other three types of symmetry – mirror, radial and translating ones. The different types of rhythms are combined with suitable color combinations. Very interesting is the use of the spiral polygons, which included golden spirals in number equal to number of the polygons’ sides. Keywords: Golden Spiral; Spiral Polygons; Textile; Design.

1. Introduction

Successive points dividing a golden rectangle into squares lie on a logarithmic spiral [1, 2] which is

sometimes known as the golden spiral. [3] The Golden spiral is shown in Figure 1.

The geometrical forms which are based on the proportion of the Golden ratio are harmonic shapes and they

are used in textile [4] and fashion design [4, 5]. The paper presents the use of the Golden spiral in textile

design.

Figure 1: The Golden or the logarithmic spiral

2. The Golden Spiral in Textile Design

Figure 2 presents a textile design which combines golden spirals using radial and translating rhythms. The

motif is a result of a radial rhythm which forms a square from four golden rectangles with golden spirals. The start points of the spirals are situated on the side of the centre of the radial rhythm. The design uses three colors’ model. Actually two of the colors are hues of one and the same color, the third color is a contrasted one. And the motif is colored by two different ways.

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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Figure 3 presents a textile design which combines golden spirals using radial and translating rhythms too.

The model uses two motifs which are results of radial rhythms which forms a square from four golden rectangles with golden spirals. In the first motif the start points of the spirals are situated on the side of the centre of the radial rhythm. In the second motif the start points of the spirals are situated on the outside side of the square. The design uses three colors’ model. Actually the three colors are hues of the one and the same color. The both motifs are colored in opposite ways. The spirals are colored in the darkest hue and the motifs are constructed around squares colored in the darkest hue too.

One of the motifs which are used in the model shown in Figure 3 is used in the textile design presented in

Figure 4. The colors are the same like the ones in the design in Figure 3.

Figure 5 shows a textile design which combines golden spirals using radial and translating rhythms. The

motif is a result of a radial rhythm which forms a square from four golden rectangles with golden spirals. The start points of the spirals are situated on the side of the outside of the square. The design uses two colors’ model. The spiral is a border between both colors in every square from the golden rectangle.

Figure 6 presents a textile design which combines golden spirals using radial and translating rhythms too.

The motif is a result of a radial rhythm which forms a quad spiral from four golden rectangles with golden spirals. The start points of the spirals are situated on the side of the center of the radial rhythm. The design uses two colors’ model. The spiral is a border between both colors in every square from the golden rectang le and the every next square in the golden rectangle is colored in opposite way.

Figure 7 shows a textile design with the use of the spiral square or the square pursuit [6] 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. [7]” The textile design in Figure 7 combines mirror and translating symmetries and uses four colors –

two hues of two basic ones.

Figure 8 presents a textile design with the use of the spiral triangle or equilateral triangle which forms three

golden spirals. [8] The creation of the spiral triangle is similar to the creation of the spiral square. The design

in Figure 8 combines mirror and translating symmetries and uses six colors – two hues of three basic ones

for the three spiral forms.

Figure 9 shows a textile design which is very similar to one which is presented in Figure 8. The difference is

that the rhythmic model in Figure 8 uses mirror symmetry and the rhythm in the textile design in Figure 9

uses radial symmetry.

Figure 10 presents a textile design with the use of the spiral hexagon. The creation of the spiral triangle is

similar to the creation of the spiral square and the spiral triangle. The design in Figure 8 uses translating

rhythms and two colors.

3. Conclusion Essentially the golden spiral is spiral symmetry or it forms spiral symmetry and for creation of beautiful and harmonic forms in the textile design it is used in combination which are based on the rhythms, results of the other three types of symmetry – mirror, radial and translating ones. The different types of rhythms are combined with suitable color combinations. Very interesting is the use of the spiral polygons, which included golden spirals in number equal to number of the polygons’ sides. Essentially the spiral polygons are radial rhythms or creations on the base radial

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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symmetry. Despite that the spiral pentagons are radial rhythms, they are used in the textile design in combination on the base mirror, radial and translating symmetries too.

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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Figure 2: A textile design using the Golden spiral on the base of radial and translating rhythms and three colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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Figure 3: A textile design with two motifs using the Golden spiral on the base of radial and translating rhythms and three

colors’ combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

6

Figure 4: A textile design using the Golden spiral on the base of radial and translating rhythms and three colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

7

Figure 5: A textile design using the Golden spiral on the base of radial and translating rhythms and two colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

8

Figure 6: A textile design using the Golden spiral on the base of radial and translating rhythms and two colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

9

Figure 7: A textile design using the spiral square on the base of mirror and translating symmetries and four colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

10

Figure 8: A textile design using the spiral triangle on the base of mirror and translating symmetries and six colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

11

Figure 9: A textile design using the spiral triangle on the base of radial and translating symmetries and six colors’

combination

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

12

Figure 10: A textile design using the spiral hexagon on the base of translating symmetries and two colors’ combination

References

5th SMARTEX-2015 Egypt (WORLD TEXTILES CONFERENCE), [ENGINEERING -

APPLIED ARTS - SPECIFIC SCIENCES] NOVEMBER 23 - 25, 2015, KAFERELSHEIKH UNIVERSITY, EGYPT.

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[1] Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York:

Broadway Books, p. 85, 2002.

[2] Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 88, 1991.

[3] Weisstein, Eric W. "Golden Spiral." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GoldenSpiral.html.

[4] Kazlacheva Z., Ilieva J. “The Golden and Fibonacci Geometry in Fashion and Textile Design”.

Proceeding of eRA 10, Piraeus, Greece, September 2015.

[5] Kazlacheva Z. “The Golden Squares in Fashion Design”. EMIT Economics Management Information

Technology, Vol. 4, No. 1, pp. 32-38, June 2015.

[6] Sharp J. “In pursuit of pursuit curves”. ISAMA 99, N. Friedman and J. Barrallo, eds. University of the

Basque Country. 1999.

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

[8] Weeks E. “Spiral Triangles”. http://www.physics.emory.edu/faculty/weeks//ideas/spiral.html. Author: Julieta Ilieva, MSc, Assistant Trakia University, Faculty of Technics and Technologies Graf Ignatiev 38, 33516, Yambol, Bulgaria Phone: (+359) 46669181 Cell Phone: (+359) 897512012

Fax : (+359) 46669183 E-Mail: zhulieta.ilieva@trakia-uni.bg