Why Geometry has played a central part in Painting - Essay Example

Why geometry has played a central part in Painting (College) What, really, is geometry? How do we perceive and understand the meaning of it and its place in Art? By using ‘Kosuthian’ method of explanation, the definition of Geometry is ‘the branch of mathematics concerned with points, lines, curves, and surfaces (In Greek geometrein means to measure the land). In addition, we could also add some key words, which are mainly associated with this discipline: shape, form, pattern, symmetry, balance, scale, system, proportion, structure, repetition. Most of the terminology we find in art and math, and obvious connection between the two of them is geometry itself. Now, both art and math involve drawing and the use of shapes and forms, as well as understanding spatial concepts, two or three dimensions, measurements, estimation, and pattern. Many of these geometrical elements are evident in artworks from all eras from the Renaissance and before, until modern day. Furthermore, geometry and art even share a vocabulary; for instance, artists use the term two-dimensional shape, while mathematicians call the same thing plane figure, what artists call three dimensional figure, for the mathematicians is known as space or solid figure. Perhaps every artistic discipline requires drawing as a means of expression or a planning tool. Drawing, for instance is a necessary planning and modeling medium in architecture. Painters have used it as a medium of expression as well as a compositional tool in paintings. Geometry had played an important role in the history of visual art. The major revolutionary discoveries in the painting of Renaissance, for instance, were a result of painter’s study and practical adoption of Euclidian geometry. With Cezanne, however, this tradition was finally suspended and painters started to question the foundations of classical painting, which resulted in their rethinking of the geometrical dimension of these foundations. Painters became aware of ‘the background’, the surface, and started applying geometry in new ways. If we can speak, metaphorically, about the inner space of painting, we could say that this space experienced immense shifts and metamorphoses mainly in the twentieth century. Painters started creating new spaces. We could compare it with creation of fictional spaces in literature (magical realism and science-fiction). For instance, Jorge Luis Borges in his fiction describes an attempt to create one such new space. My main aim in this text, however, is to explore the relationships and importance of geometry in painting. In order to better understand these relationships we need to look back in time into the “science of space”. I will aim to include three chapters in this text, the first dealing with the study of geometry, symmetry and their basic, most important properties and its uses in earlier movements of art in order to present the most relevant examples of works into the second chapter which will deal with analysis of works of art (mainly paintings). The third and final chapter will deal with answering the question; “Why geometry has played a central part in painting?” “It was then that all these kinds of things thus established receive the shapes of the ordering one, through the action of ideas and numbers”- Plato. Plato’s philosophy of the universe was centered on the Deity. He believed that the universe is built out of four elements; earth, fire, water and air (as Empedocles before him), which takes a form of geometrical solids (earth- cube, fire- tetrahedron, water- icosahedron, air- octahedron) which then can brake further into triangles. As mentioned above geometry means earth measure. As we shall see the journey is from the single point into the line, out to the plane, to the third dimension and beyond eventually returning to the point again. Like the elements of its sister subject music, it is an aspect of revelation in a creation myth in itself. Number, music, geometry and cosmology are the four great liberal arts of the ancient world. These simple universal languages are as relevant today as they have always been and may be found in all cultures without disagreement. In geometry the notion of proportion is one of the most basic, most important and the most difficult to deal with precision because it is often confused with the notion of ratio. “The quantitative comparison between two things” is a simple definition of ratio. The method by which in a complex plan or design the proportions were linked so as to get the right correlation between the whole and its parts was call by the Greek architects “symmetry”. The result obtained where this method was successfully applied was the “eurhythmy” of the design and of the building. The terms of rhythm and eurhythmy are generally associated with the arts working in the time (poetry and music), and the notion of proportion with the arts of space (architecture, painting, drawing, decorative art). “The Greeks did not care for these distinctions; for them, for Plato in particular rhythm was a most general concept which dominates not only aesthetics but also psychology and metaphysics. For them indeed architecture was not only “frozen music” but living music and if architecture is petrified as frozen music so is music drawing in time. In reality they are just five regular three-dimensional solids, known as the five Platonic solids. The first solid is the tetrahedron, the second solid is the octahedron, the third is the cube, the fourth is the icosahedron and the last fifth element is the dodecahedron. We will later see that these five solids are connected to each other in a subtle way. It is worth to mention that if we take the centers of a figure of the surfaces limiting one body, we obtained the other one. These operations can be repeated indefinitely producing alternating ever-growing pulsation of growth in which lines, surfaces, volumes are ruled by the Golden section of π (Pi) proportion. “But it is impossible to combine satisfactorily two things without a third one we must have between them a correlating link such as the nature of proportion.” –Plato The Golden section is one of the three simple proportions found in the early polygons. The bottom picture shows a golden section spiral very common throughout the natural world. “The ratio between the greater and the small part is equal to the ratio between the whole and the greater part. The Golden section rectangle is widely used in painting, drawing and architecture constructed from the midpoint of the side of the square. Also the design of a sacred building requires the architect to marry the universal symbolism of the geometrical moves he or she is making with the specific religious language. For instance Winchester Cathedrals axis points 72 from North Creighton creating a magical magnetic pentagram. The Golden section also places a dominating part in the proportions of the human body which was perhaps recognized by the Greek sculptors. The regular octagon has played a great role in architecture and was used in the planning of many churches and mosques especially in the Byzantium, Arab and Romanesque schools (San Vitale of Ravenna, Carolingian cathedral of Aachen, Mosque of Omar in Jerusalem and others). The star octagon composed of two overlapping squares has been used as geometrical patterns of ornamentation in Arab, Muslim and Indian Moghul decorative art. The circle is often in Gothic designs subdivided into 20 parts instead of 10 but this leaves the same symmetry based on the Golden section. There are thirteen semi regular solids, they are called Archimedean solids. The most important of the thirteen is the cub octahedron, which plays a predominant part in crystallography. The cub octahedron has played an important part in architecture, especially in Byzantium and Muslim architecture and solved the problem of setting a dome on a cubicle supporting frame. “The vertices of the cub octahedron coincide with the points of contact of six tangent orthogonal circles inscribed on the square faces of degenerating cube” (Santa Sophia). This polyhedron is the only one among the 13 Archimedean solids which can fill a space by repetition without intervals. The science of space was the basic discipline the aesthetical frame and guide for the painters and architects of the first Renaissance. The painter-geometers of the Renaissance were interested in them as well as in the five regular Platonic solids. In 1492 Pierre Della Francesca dedicated the Treatise de Guinque Corporibus to the duke of Urbino. The Renaissance author who took most interest in Archimedean solids was the old known Daniel Barbaro, Patriarch of Aquileaand Venetian diplomatist. The first attempts of systematically incorporating geometry in art were made in the representation of three-dimensional world. The Italian masters Giotto Di Bondone and Duccio Di Buoninsegna (Byzantine, Medieval and Gothic periods) began to explore the idea of depth and volume in their art and can be credited of introducing the early form of perspective, but still using shadows and color to create an illusion of depth, which was still far from the kind of realistic space, which FillipoBrunelleshi depicted in his works by using linear perspective; the system he used projected the illusion of depth onto two-dimensional plane by use of ‘vanishing point’ to which all lines converged, at eye level, on the horizon. So in the early period of Renaissance artists started to use the ‘Brunelleshian’ system or rather what is known as Euclidean Optics. Masaccio was the first who demonstrated full command of the new rules of perspectives. The figures in his paintings have volume and the architecture and landscapes realistically recede into the distance. Many others as we know after him; Leonardo da Vinci, Michelangelo, Raphael, Botticelli, Donatello and Titian were able to create realistic world representing spaces, to depict the full beauty of nature on the flat. The developments were not limited to Italy, it spread throughout the Europe, particularly towards Netherlands with the work of Hugo Van Der Goes and Jan Van Eyck. The artists were able to translate places in space on the two dimensional background in the early stage of Renaissance, but it was only an interpretation from a very realistic standpoint. It lasted till the beginning of Modern art. Towards the end of the 19th century French painter Paul Cezanne began to question the underlying structure of the objects. At points his work became almost abstract, pigment was applied on the canvas with palette knife, usually thick layers, and the naturally occurring forms were simplified to their essential geometric shapes. But most importantly he started to ignore the laws of classical perspective, allowing each object to be independent within the space of a picture while letting the relationship of one object with another to take precedence over traditional single-point perspective. This was perhaps the beginning of the end of academic composition which followed the long established rules of perspectives. Then, after him, Pablo Picasso (form) – a breakaway artist from the traditions of perspective; Henri Matisse (color), still using compositions based on the surrounding world, he created his own flat space where objects were distorted and refigured to fit their place within the composition and color was rather used more as an independent structural object. Also, Wassily Kandinsky (abstraction) totally abandoned a contact with reality and gave form and color different meaning. Then, Piet Mondrian; the forms he used where colored often in three main colors, boundaries of the shapes were marked by black lines. Finally, Kazimir Malevich, who used simple geometric shapes, such as square and circles within a limited range of color (‘white on white’, ‘black circle’, ‘black square’). As we see, the ‘science of space’, or Geometry as we know it, started to be used in early Renaissance, taking a realistic approach but rarely revealing the background of the process of how the illusion of such space was achieved. Experimentation and innovation overtook the traditional perspective as the driving force in art when geometry was applied in more radical way, so to speak. The essence of the discipline started to shine more directly towards the viewer in modern art, appearing in full forms, shapes, color, lines, etc. Geometry has played a key role in painting as it has incorporated use of lines in paintings. These lines vary in width, length, curvature, color or direction. A classic example where lines have been incorporated is the painting of “still life with bread and fruit,” painted by artist Diego Rivera. Diego Rivera had a liking for art especially using geometric shapes. He even uttered that “cubism had corrupted the way I see reality.”1 This painting which displays a table lay with fruit, bread, a cutting object drinking and serving utensils is characterized by different geometric shapes and forms. There is a table cloth draping over the left side of the table which is composed of triangular shapes. There are pears and apples in spherical shape. The light and shadowy areas in the painting appear as shapes. Rivera has used lines to create shapes that form the various items on this painting. Artist Laura Long also incorporates use of lines in her painting; Quilt “log cabin “pattern2. This quilt forms a rectilinear design whereby all parts appear to be moving in or forming straight lines. These lines are seen as diagonal strips of color. Lines are also used in perspective geometry to create optical art by creating line designs and using symmetry. Repetition and pattern are utilized in works of art in many ways. Repetition refers to recurrence of an element of art say, shape or an object. Pattern is a combination of different elements of art or objects arranged in a recurring and regular manner. An example of repetition and pattern in a piece of art is the Buddhist mandala (Taizokai/ womb world mandala)3. This is a hanging scroll with a center square which represents the young stage of Vairocana Buddha. Repetition in this art is evident at the center and the immediate area surrounding the center where there is repetition of figures. These figures are different in size but they recur in an ordered, regular pattern. In Frank Lloyd’s Table Lamp from the Susan Lawrence Dana House, Springfield, Illinois, pattern is displayed in form of radial symmetry4. He uses the geometric concepts of radius, diameter and circumference to form this symmetrical design. This design radiates from a central axis following a regular, repeated pattern. Wright discovered pattern using basic geometric shape at a very tender age while playing with a set of blocks his mother gave him. “I used to love to sit down at the drawing board with a T square and a triangle and concoct these patterns” Wright said in 1952, “I evolved a whole language of my own with those things.” Shapes or plane figures are also key elements of arts used in painting. Shape requires the use of two-dimensional space in which all points lie in the same plane and is defined by edges. Shape is defined by other elements of art such as line, space, color, texture and value. Geometry also introduced the use of solid figures or forms/space. Solid figures are three dimensional that is they have length, width and height. The use of solid figures brought about the emergence of cubism, as a way of portraying reality, atmosphere, light and perspective. This was achieved by demonstrating a 2-dimensional on a 3-dimensional plane. There are three types of cubism; primitive cubism, analytical cubism and synthetic cubism. Primitive cubism began from 1907 to 1908. It was kicked off by Pablo Picasso in the painting D’avignog Young Ladies. Pablo Picasso’s painting; the vase, bowl, lemon is an example of a painting in this era. Analytical cubism was from 1908 to 1912. During this period, artists explored pure forms of subjects by breaking them down into flat planes and arranging them in complex overlapping relationships. A classic painting that employed this technique was Picasso’s painting; Ma Jolie5. Synthetic cubism began from 1912 to 1920’s. The paintings were more realistic looking but the use of geometrical shapes remained. Geometric objects were being mixed with regular objects and this time bright colors like yellows, reds and greens were used. The Guitar by Juan Gris is a classic example of a painting in this era. Geometry introduced the aspect of balance in paintings. Balance is the manner by which elements are arranged to bring harmony and equilibrium. There are three types of balance which are symmetry, asymmetry and radial symmetry. Symmetry is the type of balance which shows identical shapes and patterns on either sides of a central boundary. Asymmetry balance does not present identical shapes and patterns when divided by a central line. Radial symmetry shows a regular repeating pattern which radiates from a central point. Frank Llyod Wright employs radial symmetry in the design of the “table lamp from the Susan Lawrence Dana House.” In Laura Long’s Quilt “log cabin” the quilt is symmetrical as it can be folded into identical halves and quarters. An example of a painting with the aspect of balance in it is a painting by BernadoDaddi; Madonna and child with Saint Helen and Peter and Saints Catherine and Paul in 13396. In this painting the mother and child are placed at the center, directly on the horizontal, central and vertical axes. There are marching figures on either sides of the central axis which displays the symmetrical balance. Asymmetrical balance is depicted in yet another painting of Bernado Daddi; Madonna and child with Saint Helen and Peter and Saints Catherine and Paul in 1339. In these painting three smaller shapes on the right balances the large figure on the left which brings about asymmetrical balance. Perspective is another element of art that is as a result of geometry. Perspective is a technique used by artist to represent a three-dimensional figure on a two-dimensional surface. A simple form of perspective is linear perspective which creates depth and distance on a flat surface. It applies a set of implied lines referred to as converging or orthogonal lines that move closer together at apparent distance until they merge at an imaginary vanishing point. Linear perspective consists of one point perspective where there is a single vanishing point or two point perspective which lead to two vanishing points. Nicholas Pousin incorporates perspective in his painting; Landscape with Saint John and Patmos (1640)7. In this painting, the ruins in the foreground a cube, a three dimensional rectangle and a cylinder are represented in a perfect perspective form, each showing a different aspect of foreshortening. The pathway vanishes into the distance giving an illusion of depth. Proportion is the final element of art brought about by geometry. Proportion deals with relationship of parts of the composition to each other and to the whole in terms of size. Leonardo da vinci’s drawing of the Vitruvian man clearly shows the proportions of the human figure8. It is recognized as a man holding out his arms and legs and appearing to have two sets. Leonardo believed that the proportions of the human body were perfect and correct. Having discussed some of the elements of art, there are several classic examples of paintings that incorporate all or most of these elements. A good example is Leonardo da vinci’s painting on the “last supper.”9 In this painting, the general disposition is shown by the rectangular table in which all the thirteen people (Christ and his twelve disciples) are drawn. To the keen eye it is evident that they are placed almost in a straight line. The entire wall surface in the dining room is subdivided into three layers; a basic layer including a door, three painted arcades above in the shape of semi circles and the painting of the last supper. The middle layer gives an illusion of a deep hall having rectangular tapestry on the sides and three openings leading into a landscape. The linear perspective points are at the head of Christ (the right ear). The body of Christ with his right and left arms extended forms the central pyramid. The geometric arrangement of the thirteen persons is symmetrical as Christ is at the center and there are six apostles on either side. “The Birth of Venus,” a famous Italian art, painted between 1482 and 1485 by Sandro Botticelli incorporated the golden ratio as a tool to design his art10. The key elements in this painting are positioned exactly at golden ration points. For instance, the horizontal golden ratio line from top to bottom crosses at the top of the sea shell. The horizontal golden ratio line from bottom to top crosses at two precise points; at the horizon, perfectly on the painting’s left side and directly through Venus’ navel. The golden ratio line running vertically through the painting from left to right falls accurately at the point at which Hora’s thumb and finger are touching. This appears as though she is holding the golden ratio proportion embedded in the painting, maybe even reaching for something divine. The vertical golden ratio line from right to left falls right where the land on the horizon meets the sea. It is also evident that her navel also lies at the golden ratio point of the height of her body. Any golden ratio point of her body created all cross exactly at her navel at the bottom of her navel. In this study, an extensive discussion on painting has been covered based with in-depth analysis of composition as well as geometry. Geometry is a fundamental part of art work as presented in the above discussion. The study reveals how this branch of mathematics has been incorporated by artists that have brought about certain components in painting which effectively strikes the viewer’s eyes. These components are best known by artists as elements of art. They include lines, repetition, shapes/plane figures, forms/ space/ solid figures, balance, perspective and proportion. Paintings are designed by ordering and manipulating these elements of art. Taking a close look at most art work in both the ancient and modern days reveal the use of geometric symbols as well as geometric constructions. This is mainly because it has incorporated certain aspects to the world of art which has improved it by milestones. Furthermore, geometry has enabled artists communicate in the best way they can though what they love most. Indubitably, that explains why the depth representation in geometric art work has so much power in it. Censoring all the art work based on the few instances portrayed in the study, we can conclude by saying that geometry has served as an impetus in artistic development. Bibliography Arts Connected. Madonna and Child with Saints Helen and Peter and Saints Catherine and Paul; The Angel of the Annunciation; Saint Francis Receiving the Stigmata; The Virgin of the Annunciation; The Crucifixion with the Virgin and Saint John. Tools for Teaching Arts. February 2009. Web. Retrieved from: http://www.artsconnected.org/resource/10165/ Ivins, M. W., Art and Geometry: A Study in Space Intuitions. Boston: Courier Corporation. 2012. LACMA Evenings for Eduators, GEOMETRY AND ART SYMMETRY, BALANCE, SCALE. Education programs at the Los Angeles County Museum of Art are supported in part by the City of Los Angeles Department of Cultural Affairs, the William Randolph Hearst Endowment Fund for Arts Education, and Rx for Reading. 2011. PP. 1-12. Print. Art history, U.S. History, World History, Ma Jolie. Web. Retrieved on: March 11, 2015. Retrieved from http://www.totallyhistory.com/ Leonardo da Vinci’s Life, Vitruvian Man, The Proportion of the Human Figure. Web. Retrieved on: March 11, 2015. Retrieved from: http://www.davincilife.com/ Leonardo da Vinci’s Life, Da Vinci the Artist. Web. Retrieved on: March 11, 2012. Retrieved from: http://www.davincilife.com/ Marin, G. R., Diego Rivera the Red. Houston, Texas:Arte Publico Press, Jan 1, 2004 Fine Arts, Design in Art: Repetition, Pattern and Rhythm. Web. Retrieved on: March 11, 2015. Retrieved from http://www.sorphia.org/ Phi 1.618: The Golden Number: Botticelli, The Birth of Venus and the Golden Ratio in Art Composition. Web. Retrieved on March 14, 2015. Retrieved from http://www.goldennumber.net/ What is perspective: The Basics of Perspective. Web. Retrieved on March 14, 2015. Retrieved from http://www.artic.edu/ Read More