In Search of Beauty – Golden Ratio.

In search of beauty – Golden Ratio

                                           

Art of the Ages was saturated with mathematics and geometry. The key to all of harmony was Golden Ratio, also known as the Divine Proportion - an aesthetic canon developed in ancient Greece. It describes a split section into two parts in such a way that the ratio of the longer to the shorter portion was equal to the ratio of the entire section of the long parts. This ratio is called the golden number and denoted by the Greek letter ‘fi’, its value is approximately 1.618.

Golden Ratio was born from the observation of the world around them - the ancient philosophers and mathematicians noticed that it occurs in geometry and nature seems to strive for it in their works. It was believed that the use of the divine proportion in works of art provide them to achieve a perfect beauty. The first of a famous artist, who had used the Golden Ratio, was Phidias, the most famous sculptor of ancient Greece. In ancient times , as well as during the Renaissance and Classicism based on the gold division determined plans temples , porticoes height and width , holes windows , doors, architectural details shapes , images , and the books.

Piero della Francesa , mathematician and Italian Renaissance painter in his frescoes combined multi-storey layouts various combinations dividing the golden triangles , rhombus, and other geometric figures. For masters “mathematical composition " belonged Renaissance genius Leonardo da Vinci. This great experimenter applied the principle of the golden ratio in his most famous work - a portrait of Genoese lady, also known as Mona Lisa. The proportions of the body and face apparition’s women are dictated by the number of fi. Other Renaissance artist Sandro Botticelli , based on the golden ratio in his own image " Birth of Venus " , subordinating its dimensions work, body composition and construction of the goddess . Also later artists inspired by the divine proportion - the great eccentric Salvador Dali painted according to the principles of the Last Supper. To this day art historians deciphers the principle figures , whose were based on works of art , seeing in them the magical properties on time, but especially his aesthetic and harmonious qualities.

The principle of the golden ratio is using in many ways. Starting from the dimensions of the image created - the relative lengths of the sides - the deployment of elements of a work plan, ending on the proportion of each component. This ancient canon is important in graphic design. For example, the company Apple Logo has been designed using six different circles so that their relations were ... 1.618 rays.

                                             

Arrangement of the elements in the art work creates relationships between them, which induces on the viewer the impression of harmony or chaos, static or dynamic, equilibrium or domination. Gold division to help identify the sizes of individual elements of the image and the image's width compared to its height. Fonts designed according to the golden division, and systems to facilitate the design of the golden ratio suppliers provide multi-functional and versatile tools and their use depends on the imagination of the designer.

Contextual and Cultural Referencing extends the historical knowledge of Golden Ratio. Fun with 

colours and geometric shapes while of activities on the Visual Communication gives a greater 

awareness of image composition and interaction between the different parts of the image. All this 

provides us, future graphics to create greater force of expression in their own projects.

Reference:

William Lidwell, Kritina Holden, Jill Butler, Universal Principles of Design: A Cross-Disciplinary Reference, 2003, Gloucester MA: Rockport Publishers.

Pentagon and the Golden Ratio

Pentagon and the Golden Ratio

The ancient Greek mathematicians began research on this, what we call today the ‘golden ratio’ because of his frequent presence in geometry. The division line in the "golden way” (the golden ratio) is a significant weight of symmetrical geometry pentagrams and pentagons. Greeks usually attributed to Pythagoras discovery of this relationship or his disciples. Pentagram inscribed equilateral with Pentagon was a symbol of the Pythagoreans.

Golden ratio is not only rectangles but keeping the ratio of 1.61 which plays an important role in 

the geometry of the pentagram where all portions intersect each other in the golden ratio. Also, 

the ratioof the shorter segment to the segment bounded by two intersecting edges (side of the pentagon

inside the pentagram) is φ, as shown illustration below.

Pentagram

Pentagram is coloured to distinguish his segments 

of different lengths. All four lengths are do himself

in the Golden Ratio. Pentagram contains ten

isosceles triangles: Five acute-angled and five 

obtuse. In all them ratio of the longer side to 

shorter side is φ. Acute-angled triangles are golden
triangles, obtuse are gold 'gnomons'.

A regular pentagon with an inscribed pentagram.

The following ratios of the lengths on the lines segments shown in the figure are equal to the golden ratio.The ‘ratio’ has become known as the golden ratio or golden section and can be found in many places in maths, architecture, art and design. Ratio of 1.61 can be used also with circles, for example, as itdid in Pepsi logo.

REFERENCES

Abrohms, Alison. Literature-Based Math Activities. 1992. New York: Scholastic Inc.

B. Burns, Marilyn. The Greedy Triangle. 1975. New York: Scholastic Inc.

C. Hickey, Mary. Big Book of Small Quilts. 1997. Oxmoor House, Inc. and Leisure Arts.

Pierra della Francesca (1406-1492)

Pierra della Francesca (1406-1492)

The fifteenth century in Italy is one of the best time in the whole history of creative art. Padua, Ferrara, Mantua, Venice, and above all, Florence were the cities whose develop extraordinary artistic activity. At that time, Piero della Francesca first used the prospect launched by the architect Brunelleschi, and wrote treatises on this subject. In his frescoes he combined a variety of multi-storey layouts golden ratio with combinations of triangles, rhombus, etc.

Piero della Francesca (1406-1492) was born in Borgo San Sepolcro 

helped Domenico Veneziano in painting the chapel in Santa Maria 

Novella. Around the year 1441 in Borgo’s Cathedral of St. John the 

Evangelist he created Baptism and few years later – executed frescoes 

in the Castello Estenseand the church of Sant'Andrea of Ferrara. In 

Rimini he met Leon Battista Alberti and their relationship had an

impact on his further interest in perspective.

Early in his career Piero became interested in the new science of one-

point perspective. The method of depicting space relied on principles 

of geometry and mathematics intrigued Piero, and he soon devoted his work to its examination. He mastered the discipline, writing treatises, poetry, and books 

on the mathematical accuracy of his perspective. Most importantly, Piero incorporated a deep sense 

of perspective and created the illusion of depth and dimension throughout his work. A standard 

attribute throughout the collection of Piero is the presence of linear lines and perspective. In one of 

his most important paintings, The Flagellation of Christ, a scene of the Savior is set on a grid of 

Greek architecture, receding into the rear of the picture plane. To emphasize this depth Piero painted 

a seemingly insignificant grouping in the front of the canvas, exaggerating the placement of the 

figures and the condensed space. He interpreted the beauty of the world as a combination of shapes 

circle, pyramids, and cones and merged his idea of space with his use of sophisticated color. Some 

revere Piero as the earliest ancestor to the modern artists concerned with simplifying objects to their 

purest form.

The History of The True Cross fresco cycle (1452 - 1456), Basilica San Francesco.


References to literature and culture with psychological tensions (contrast), and symbols show 
Piero dell Francesca as intellectual painter. Despite this, after his death, his painting was relegated
to second place. Once again it was discovered in the nineteenth century and early twentieth boosted
after the success of Cubism and Neo Impressionism. 

References:

Carr-Gomm, S. The secret Language of Art, 2001, England, Duncan Baird Publishers.

Parramón, J. M How to Draw, 1991, Barcelona: Paramón Ediciones, S.A.

Parramón, J.M.  How to Drad in Perspective, 1988, Barcelona; Paramón Ediciones, S.A.

www-history.mcs.st-andrews.ac.uk/Biographies/Francesca

Giotto di Bondone (1266-1337)

Giotto di Bondone (1266-1337)

Giotto di Bondone, actually Angiolo di Bondone, Italian architect and painter in the Renaissance, one of the first proponents of perspective. According to the chronicler Vasari, he ‘rejected a Byzantine mannerism and has encouraged the realism’ in way that the line converge as in nature, toward the point of projection. (Parramón, p.15. )However, his perspective was still very intuitive compared to what will happen in the bloom of the Renaissance.

A legend says, that as a young boy Giotto was a shepherd and in free time he was doing amateur drawings which were soon spotted by the famous architect Cimabue. These stories, however, should be considered a bit of a distance. In fact, Giotto studied painting at the side of his master Cimabue and during this period, probably he was travelling to Rome and Pisa.

In 1288-1292, first time he demonstrated his talent at work on the frescoes in the Basilica of St. Francis of Assisi. In the years 1303-1305 he worked in Padua, where he painted frescoes Scrovegni Chapel. In 1310-1320 he lived in Florence, where he performed the frescoes at the Basilica of Santa Croce, designed and built a bell tower. In 1328 the king of Naples invited him to decorate the chapel and halls of the palace. In 1334 he returned to Florence, where he was honored by the city authorities being appointed as a chief architect to Florence Cathedral. His last known work (with assistants' help) is the decoration of Podestà Chapel in the Bargello, Florence. In his final years Giotto had become friends with Boccaccio and Sacchetti, who featured him in their stories.

Expulsion of the Devils from Arezzo (1295 - 1299)

The tenth of twenty-eight scenes of the fresco cycle of the stories of St. Francis of Assisi.

References:

Parramón, J.M. How to Draw in Perspective, (1988) Barcelona: Paramón Editions, S.A.

www.giottodibondone.org/biography.

Leaonardo da Vinci - a new stage in the art of the West.

                         

  Leonardo da Vinci (1452-1519)

Self-portrait (ca.1512)
chalk on paper

A tireless inventor, writer, botanic, surveyor, universal genius. Innovator in all areas of creativity and began, with the invention of chiaroscuro, a new stage in the art of the West. His sketches and notes reveal to an inexhaustible interest in geometry, composition and perspective. He experimented all known methods, reaching the admirable results. It was interested movement, the expression of, chiaroscuro, linear perspective, colour and air. His works, together with his notebooks, which contain drawings, scientific diagrams, and his thoughts on the nature of painting, compose a contribution to later generations of artists.

In 1466, at the age of fourteen, Leonardo was apprenticed to the artist Andrea di Cione known as Verrocchio, whose workshop was"one of the finest in Florence". Others famous painters apprenticed or associated with the workshop include Domenico Ghirlandao, Perugino, Botticelli, and Lorenzo di Credi. In 1483-1499 Leonardo da Vinci was in Milan court of  L. Sforza, then in Moro, Florence (1500-1506), again in Milan ((1506-1513), Rome (1513-1516) under the care of G. Medici, brother of Pope Leo X. In 1516, he was invited by Francis I to France.

From the first period of the Florentine come The Adoration of the Magi, St. Jerome (both not gradu-ated), Annunciation, and studies to Madonna with a kitten. With the period of the court of Milan come; Lady with an Ermine .Virgin of the Rocks. The Last Supper - Leonardo's most famous art painted for the refectory of the Convent of Santa Maria Della Grazie. In the second period of the Florentine he worked over the image of the Mona Lisa (1503 -1506). In the second period of Milan such as ima-ges were formed as: St. John the Baptist, Bacchus and drawing a self-portrait.

During his first stay in Milan, Leonardo da Vinci, made a systematic study in the field of botany, mathematics, optics and mechanics. There were created parts of the Treaty about painting, architecture and anatomy, optics and mechanics. In the second period the Florentine continued scientific work and researching the primary forces of nature, covering all cosmologies. He has developed numerous projects, much of leading his epoch. In 1490 years he created Vitruvian Man - a study of the proportions of the human body. Drawing is accompanied by text, from which it follows that figure is illustrative of the Treaty of Ten Books about Architecture Vitruvius, dedicated to the proportions of the human body.

After his death, his disciple and friend, F. Melzi gathered 19 works of Leonardo in the books. Interestingly, he found on the notion of the unity of science and art, of which Leonardo was extremely loyal in his live and his oeuvre.

Reference:
www.biography.com/people/leonardo-da-vinci

From the Gold Division to Fibonacci Numbers

From the Gold Division to Fibonacci Numbers

In 1202, Italian mathematician Leonardo Fibonacci developed a series of numbers called the Fibonacci sequence. By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two:  0, 1, 1, 2, 3, 5, 8, 13, 21, etc. Therefore, value of each number is calculated by using what you already have calculated so far, without having to memorize all the previous values ​​- because the last two are suffice. Fibonacci sequence is the first the known of this kind sequences.

As a result of dividing each of the numbers of its predecessor in the sequence is obtained quotient which oscillating around 1.618 (Golden Ratio). With increasing numbers decrease 

deviation from this value. The inverse of 1.618 is 0.618. In connection with this, the factor of each

 number divided by the next number oscillate around 0.618. Between any two numbers separated by

a single number occurs ratio of 2.618 and its inverse, 0382. The same procedure can be repeated for a number of more distant from each other. For example, numbers separated by three positions have coefficients 4.236 and 0.236; number four positions away have proportions expressed by factors 6.853 and 0.146.

Applications include computer algorithms such as the Fibonacci search technique and the

Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting 

parallel and distributed systems. They also appear in biological settings, such as 

branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone.

Scientists have concluded that the phenomenon, whose structure is based on the Fibonacci 

sequence, give pleasure to the senses of sight and hearing beings human. The proportions 

gold ratio based on the Fibonacci sequence were used by Leonardo da Vinci in his paintings as well as by Botticelli.Gold proportions were also used during the climb the pyramid of Cheops at Giza and the Parthenon 

in Greece.

Reference:

Abrohms, A. Literature-Based Math Activities, 1992, New York: Scholastic Inc.

Barack Obama Poster

Barack Obama Poster

This Shepard Fairey acrylic paint is the most widely distributed version of Barack Obama poster and came to represent his 2008 presidential campaign. Design was created in one day and Fairey sold 350 of the posters on the street immediately after printing them, and the image became iconic, one of the most widely recognized symbols of Obama's campaign message. In 2009 Fairey's Obama portrait was feathered in  the book Art for Obama: Designing Manifest Hope and the Campaign for Change.

Interestingly, the poster was  more often associated with autocrats and dictators, just like Lenin. There is an opinion that Fairey transformed the photograph and created a powerful new, radically different meaning. These trivial changes makes creation process not clear and are behind the poster. Fairey found ab photograph of Obama using search and creating the original poster design in a single day. In interviews, he has said that he made various alternations to the image he used and that the poster is hand-illustrated image. In fact, Fairey produced two other versions, based on different photographs, officially on behalf of Obama campaign. He himself was commissioned to create a number of works in the same style.

According to Steven Heller, graphic designer, the poster was inspired by Social Realism and, while widely praised as original and unique, can be seen as part of a long tradition of contemporary artists drawing inspiration from political candidates. Doubtless, Fairey primary objective was to depict Obama in a way that would increase his chance of winning. Using patriotic palette such as red, white and blue, and eyes gazing upward, create political pose that would elevate him to iconic status. Eyes on the horizon and soaked face in red-and-blue create optimism that Obama could be a constructive figure enough to build hope.

REFERENCES:

Heller, S. Vienne, V. (2012) 100 ideas of Graphic Design, London: Laurence King Publishing Ltd.

law.marquette.edu/.../the-obama-“hope”-poster-case 

www.gq-magazine.co.uk/.../shepard-fairey-obey-hope-art-posters-interview