254 chapter 10 proportion - janessa friesen · 254 chapter 10 proportion figure 10.1 this painting...

254 CHAPTER 10 Proportion

� FIGURE 10.1 This painting is a fresco. Italian for “fresh,” fresco is an art technique in which paint is applied to a fresh,or wet, plaster surface. Examine the size of the figures depicted in this fresco. Is this depiction always realistic?

Diego Rivera. The Making of a Fresco Showing the Building of a City. 1931. Fresco. 6.9 x 9 m (22’7” � 29’9”). Located at the San Francisco Art Institute, San Francisco, California. Gift of William Gerstle.

Figure 10.1 was paintedby the Mexican artist

Diego Rivera (1886–1957). At age 21, Rivera went to study art inEurope, where he met Paul Cézanne and Pablo Picasso. Returning toMexico in 1921, Rivera rejected what he had learned. He chose insteadto imitate the simplified forms of his pre-Columbian ancestors inMexico. Rivera also became a champion of the rights of the workingclass. Social themes inspired him to create large mural paintings. Hismurals, which adorn the walls of public buildings, all have political orhistorical themes.

Analyze. The mural in Figure 10.1 shows scenes of urban construction.Notice the large male figure in the center. Form a conclusion about themeaning and historical context of this figure. Who or what does he represent?

You may be taller than some students in your art class,

shorter than others. Distinctions like these involve

proportion, or relative size. As an art principle, proportion

can direct the viewer’s eye to a specific area or object in

an artwork.

In this chapter, you will:

Explain and recognize the Golden Mean.

Identify scale and proportion in artworks.

Create visual solutions using direct observation

to reflect correct human proportions.

Compare and contrast the use of proportion in

personal artworks and those of others.

CHAPTER 10Proportion

255

The Golden Mean

Through the ages, people have sought an ideal of harmony and beauty.One way they have tried to capture this ideal is through correct propor-

tion. Proportion is the principle of art concerned with the size relationship of onepart to another. Artists and architects have looked for a ratio (a mathematicalcomparison of sizes) that would produce an ideal form for figures and struc-tures.

The ancient Greek philosopher Pythagoras found that he could applymathematical equations to both geometric shapes and musical tones. If this was so, he thought, there must also be a way to explain other things—even the universe—in mathematical terms.

Euclid, a Greek mathematician, discovered what he considered a perfectratio, or relationship of one part to another. He called this ratio the GoldenSection, or Golden Mean, a line divided into two parts so that the smaller line hasthe same proportion, or ratio, to the larger line as the larger line has to the whole line(Figure 10.2). With this ratio, the ancient Greeks felt they had found theideal proportion. It was used to control the relationship of parts in their sculp-ture, architecture, and pottery. In math, this ratio is written 1 to 1.6 or 1:1.6.

The Golden Rectangle (Figure 10.3)had sides that matched this ratio. Thelonger sides were a little more than oneand a half times as long as the shortersides. This ratio was thought to be themost pleasing to the eye. If you lookclosely at Leyster’s The Concert (Figure10.4), you can see that the wall and thetwo figures on the right side of the workis a square, while the wall and the sin-gle figure on the left is the smaller sec-tion of the Golden Rectangle.

The Golden Mean is also related to thehuman figure. If you divide the averageadult male body horizontally at the navel,the two body measurements that result(head to navel � a and navel to toes �b) have a ratio of 1 to 1.6 (Figure 10.5).


LESSON 1

� FIGURE 10.2 The ratio of the Golden Mean is 1 to 1.6.

� FIGURE 10.3 The Golden Rectangle is interestingto study. If you divide it into two shapes, one of whichis a square, the remaining shape will always be a smallerGolden Rectangle. This new Golden Rectangle can bedivided again and again.

Vocabulary

proportionGolden Mean

The secret of the Golden Mean wasforgotten with the fall of AncientGreece. The ratio was rediscovered,however, during the Renaissance, and abook was written about it. This time theratio was called the Divine Proportion,and it was thought to have magicalqualities.

Since that time, some artists havechosen to use the Golden Mean as thebasis for their compositions. Others,unaware of the mathematical ratio,used the Golden Mean just because thatarrangement of parts looked good. Mostartists now reject the idea that only thisone rule can define the “correct” pro-portions for all works of art. The ratio,however, is found in visual art so oftenthat it is hard to ignore its importance(Figure 10.6, on page 258).

1 a

1.6 b� FIGURE 10.5The relationship ofthe Golden Mean tothe human body.Section a extendsfrom head to naveland section bextends from navelto toes.

� FIGURE 10.4 Judith Leyster has used the proportions of the Golden Mean to organize thispainting. Look at the line dividing the back wall. The section on the right forms a perfect square.The section on the left is a Golden Rectangle. It can be divided just like the smaller section of the diagram in Figure 10.3.

Judith Leyster. The Concert. c. 1633. Oil on canvas. 109.2 � 167.6 cm (43 � 66�). The National Museum of Women in the Arts, Washington, D.C. Gift of Wallace and Wilhelmina Holladay.

LESSON 1 The Golden Mean 257


Notice how Bellowshas used the Golden Rec-tangle and the diagonal ofthe square in the rectangleto give this action paintingstability. He has used thevertical line for his stand-ing figure and the diagonalline to help him place theleaning figure. Can you findthe square in the smallrectangle? Can you findany other artworks thatuse the Golden Mean?Many of them are verysubtle and hard to notice.

Using the Golden Mean to Organize an Active PaintingLOOKING

CLOSELY

� FIGURE 10.6

George Bellows. Both Members ofThis Club. 1909. Oil on canvas. 115� 160.3 cm (451�4 � 631�8�).National Gallery of Art,Washington, D.C. © 1998 Board ofTrustees. Chester Dale Collection.

LESSON 1 The Golden Mean 259

Many people looked to the humanbody as a source for perfect proportions.Artists during the Golden Age of Greecebelieved that the human body was thetrue expression of order. Statues createdduring that time were not realistic por-traits of real people. The artists of theperiod showed the ideal form ratherthan the real form (see Figure 13.3,page 353).

In the first century B.C., Vitruvius, aRoman writer, determined typical ratiosfor human proportion. These were laterused by Leonardo da Vinci and otherRenaissance artists. The twentieth-century architect Le Corbusier (luh-kor-boo-see-ay) applied human dimensionsto architecture and city planning (Figure 10.7).

Check Your Understanding

1. What is the Golden Mean?2. Describe the Golden Rectangle.3. What is the ratio of the Golden

Mean?4. How does the Golden Mean apply

to the body?

� FIGURE 10.7 Le Corbusier has been called the poet of the apartment house. This building has many of the features of a resort, such as a kindergarten and nursery, a roof garden, children’s swimming pool,gymnasium, and snack bar. Lead sheets were placed between the walls to soundproof the apartments.

Le Corbusier. Unité d’Habitation. Marseille, France. 1947–52.

LESSON 2

Scale

Scale is much like proportion, but there is a difference. Proportion refers tothe relationship of one part to another. Scale, on the other hand, refers to

size as measured against a standard reference, such as the human body. A 7-footbasketball player may not look tall next to other basketball players. The playerwill look tall, however, when you see him in scale—that is, compared with acrowd of people of average height.

In art there are two kinds of scale to consider. One is the scale of the workitself. The other is the scale of objects or elements within the design.

The pyramids of Egypt are of such large scale that people are overwhelmedby their size. These pyramids were designed to be large to express the eternalstrength of Egypt.

Wall paintings inside a pyramid depict important people in a larger scalethan less important people. The tomb painting Nakht and Wife (Figure 10.8)depicts stories about the priest Nakht and his wife. They watch their busy servants hunting, fishing, and farming on the priest’s land. In the painting,the figures of the priest and his wife are much larger than the servants. Whenfigures are arranged in a work of art so that scale indicates importance, the artist is

using hierarchical proportion. Thisarrangement disregards the actual sizeof figures and objects in order to indi-cate rank in a society. Use of scale toemphasize rank appears in the art ofmany cultures (see Figure 10.10, page 262).

Actual works of art are usually muchlarger or much smaller than they appearto be when you look at photographs ofthem. You may have seen photos with ahuman hand or a human figure addedfor the purpose of showing the size ofthe objects in relation to human scale.Without some sort of measure, no illus-tration in any book can convey theeffect of the scale of a work of art.

Some works that seem monumentalare really quite small in size. This is whythe dimensions are always listed in thecredit line of the work. Try to visualizethe size of a work in relation to yoursize. Imagine how it would look if itwere in the room with you.

Vocabulary

scalehierarchical

proportionforeshortening


� FIGURE 10.8 The servants in this painting are not all the samesize. Two figures are as large as the priest and his wife, some are halftheir size, and some are even smaller. The painting uses hierarchicalproportion. The more important figures are larger than the lessimportant figures.

Egyptian, Thebes. Nakht and Wife. Copy of a wall painting from the Tomb of Nakht.c. 1425 B.C. 2 � 1.5 m (6.5 � 5�). Egyptian Expedition of The MetropolitanMuseum of Art, New York, New York. Rogers Fund, 1915 (15.5.19 e).

Claes Oldenburg often uses scale tomake you look at ordinary objects with anew perspective. He created a 45-foot-tall pair of binoculars, a soft saxophonethat is 69 inches tall, and a 45-foot-tallclothespin (Figure 10.9). Can you imag-ine what it would feel like to stand infront of a clothespin that is over eighttimes taller than you?

Variations in scale within a work canchange the work’s total impact. Forexample, interior designers are con-cerned with the scale of the furniturethat is to be placed in a room. Thedesigner considers the scale of the spaceinto which the furniture will be placed.The needs of the people who will use thespace must also be considered. An over-sized, overstuffed sofa would crowd asmall room with a low ceiling. However,the same sofa would fit comfortably in alarge hotel lobby with a four-story ceil-ing. The large scale of the lobby wouldmake the size of the sofa look right.

LESSON 2 Scale 261

Experimentingwith Scale

Applying Your Skills. Create a small col-lage scene using magazine cutouts of peo-ple, furniture, and hand-held objects such asbooks, combs, pencils, hair dryers, anddishes. Arrange the cutouts on a smallsheet of paper using realistic, accuratescale. All of the objects in the scene shouldbe in scale with the people, and all of thepeople should be in correct proportion toeach other.Use perspective techniques andarrange things in depth to create an accu-rate scale.Draw a background environ-ment for the scene using water-basemarkers, colored pencils, or crayons.

Computer Option. Use digital hard-ware such as a camera, scanner, or videocamera and accompanying software tocapture a variety of photographs of peo-ple and objects. Use the Selection tooland Copy and Paste commands to assem-ble a computer collage that shows unreal-istic scale. Apply the tools of your choiceto manipulate the images. Images can beselected from many other sources suchas a CD-ROM or the Internet. If you donot have these capabilities, use the draw-ing and painting tools of your choice tocreate a surrealistic scene.

� FIGURE 10.9 An ordinary clothespin takes on a whole new meaning when it is 45 feet tall and installed in a plaza in front of the PhiladelphiaCity Hall.

Claes Oldenburg. Clothespin. 1976. Cor-Ten Steel. Height:13.7 m (45’). Centre Square, Philadelphia, Pennsylvania.


Drawing HumanProportions

In Western art, realistic representationof people has been the dominant stylefrom the Renaissance to the twentiethcentury. However, many artists aroundthe world use symbolic proportionsrather than representational accuracy. To the Benin people of West Africa, thehead represented life and intelligence.The prosperity of the Benin peopledepended on the head of the Oba, thedivine ruler. In Figure 10.10 the head of the Oba is one third of the wholebody. This demonstrates its symbolicimportance.

FiguresPeople come in a variety of sizes and

shapes. Categories for clothes sizes—husky, petite, tall—are just one indica-tion of the many different shapes andsizes of people.

Although they vary in height andwidth, most people do not vary withregard to proportion. Many basketballplayers, such as Wilt Chamberlain, aretall. Jockeys, such as Willie Shoemaker,are usually small and light. In Figure10.11, notice that Chamberlain’s arms,legs, and torso have the same propor-tions as those of Shoemaker. Body pro-portions cannot be defined in inches or

� FIGURE 10.10 In the art of the Benin people, symbolicproportions were used. Notice how large the head of theOba (in the center of the work) is in proportion to the restof his body.

Nigeria, Edo. Court of Benin. Mounted King with Attendants. Sixteenth toseventeenth centuries. Brass. Height: 47.9 cm (187�8�). The MetropolitanMuseum of Art, New York. Gift of Mr. and Mrs. Klaus G. Perls, 1990.(1990.332).

� FIGURE 10.11 Wilt Chamberlain, an NBAstar, was a seven-time consecutive winner of theNBA scoring title from 1960 to 1966. He retiredin 1974. Willie Shoemaker, an American jockey,won 8,833 races in his career and is consideredthe best rider in thoroughbred racing history.Chamberlain is over 7 feet tall, while Shoemaker isapproximately 5 feet tall.

Annie Liebovitz. Wilt Chamberlain and Willie Shoemaker.Photograph.

LESSON 2 Scale 263

� FIGURE 10.12Average body proportions.

� FIGURE 10.13 Giotto was thefirst artist to make a flat surface appearthree-dimensional by using shading. Hewas the first to attempt realism. Thechild in this painting looks awkward, likea little adult. This is because Giottoused incorrect proportions to depictthe child.

Giotto. Madonna and Child. 1320–30. Paint onwood. 85.5 � 62 cm (335�8 � 243�8�). NationalGallery of Art, Washington, D.C. © 1998Board of Trustees. Samuel H. Kress Collection.

1

2

3

4

5

6

7

centimeters. They can only be definedin ratios of one part of the body toanother.

The unit usually used to define theproportions of an individual figure isthe length of the head from the chin tothe top of the skull. The average adult isseven and one-half heads tall (Figure10.12); a young child is five or six headstall; and an infant is only three headslong. Many artists use adult proportionswhen drawing an infant, and the paint-ing looks strange because the head issmall in relation to the rest of the body.In Giotto’s (jot-toe) painting Madonnaand Child (Figure 10.13), the childlooks like a miniature adult because ofproportion.


Sometimes an artist may purposelydistort proportion to make a drawinglook more realistic. If a person is point-ing at you, the arm from the fingertipsto the shoulder will look shorter than itactually is. In a painting, an artist willuse a technique to visually shorten thearm. Foreshortening is to shorten anobject to make it look as if it extends back-ward into space (Figure 10.14).

HumanProportions

Applying Your Skills. Use the length ofyour head (from the bottom of your chinto the top of your skull) as a unit againstwhich to measure the rest of your body.In this way you can calculate the relation-ship, or ratio, of all parts of your body toyour head.You may need a friend to helpyou obtain accurate measurements.Determine the number of head lengthsthat each of the following represents:total height, chin to waist, waist to hip,knee to ankle, ankle to bottom of bareheel, underarm to elbow, elbow to wrist,wrist to tip of finger, and shoulder to tipof finger. Record the ratios and create adiagram or chart to show your findings.Compare your findings with those of

� FIGURE 10.14 Siqueiros used foreshortening inthis painting to dramatically exaggerate his reach. Itis as if the artist wants to grab everything he can.His hand becomes a burst of superhuman energy.

David Alfaro Siqueiros. Self-Portrait (El Coronelazo). 1945.Pyroxylin on Masonite. 91 � 121 cm (3513�16 � 475�8�). Museode Arte Moderno, Mexico City, Mexico. © Estate of DavidAlfaro Siqueiros. Licensed by VAGA, New York, NY/SOMAAP/Mexico City.

Heads and FacesAs you read this section, look in a

mirror or at a classmate to check theexamples discussed.

The front of the head is approxi-mately oval. No one has a head that isperfectly oval—some people have nar-row chins, and some have square jaws.

A face is approximately symmetrical.It has a central vertical axis whenviewed from the front (Figure 10.15). Ifthe face turns away from you, the axiscurves over the surface of the head. Youcan divide the head into four sectionsalong the central axis. This is done bydrawing three horizontal lines thatdivide the axis into four equal parts, asshown in Figure 10.15.

your classmates. Find averages for theclass, because the ratios will not beexactly alike.

Computer Option. Use video digitiz-ing software and a video camera or ascanner to capture a variety of pho-tographs of people and objects. Clip artand CD-ROMs can also be used. If you do not have these capabilities, use thedrawing tools of your choice to createyour images. Use the Selection tool andthe Copy and Paste options to assemble a computer collage using unrealistic scale.Use the tools of your choice, such asResize, to manipulate the images. Create a surrealistic scene.

LESSON 2 Scale 265

The top fourth of the head is usuallyfull of hair. The hair may start above thetop horizontal line, or it may fall belowit if the person wears bangs.

The eyes usually appear on the cen-tral horizontal line. They are at the cen-ter of a person’s head. Notice the widthof the space between the eyes. Howdoes it relate to the width of one eye?The bottom of the nose rests on the low-est horizontal line, and the mouth iscloser to the nose than to the chin. Usethe sighting technique to determineother relationships, such as nose width,mouth width, and ear placement.

When you view a head in completeprofile, or from the side, all of the verti-cal proportions remain the same as inthe front view. However, both shapeand contour change. Try to discover thenew ratios (Figure 10.16). Notice therelationship between the distance fromthe chin to the hairline and the distancefrom the front of the forehead to theback of the head. Can you find a ratio tohelp you locate the ear in profile? Studythe contour of the front of the face.Which part protrudes the most? Noticethe jawline from the chin to the ear andthe relationship of the neck to the head.In Figure 10.17, the artist has drawn

� FIGURE 10.15 Facial proportions. � FIGURE 10.16 Profile proportions.

� FIGURE 10.17 The center face in this drawing is ayoung woman whom Gauguin painted on his first visit toTahiti. These serene faces with blank eyes look like ancientstone heads sculpted in Egypt or Mexico. The local Tahitianpeople were the inspiration for many of Gauguin’s paintings.

Paul Gauguin. Tahitians. c. 1891–93. Charcoal on laid paper. 41 �31 cm (161�8 � 121�4"). The Metropolitan Museum of Art, New York, New York. Purchase, The Annenberg Foundation Gift. 1996. (1996.418).



1. What is scale?2. What are the two kinds of scale pre-

sent in a work of art?3. Describe hierarchical proportion.4. How does the credit line help you

understand the scale of an artwork?5. Explain foreshortening.

Drawing the Head

Creating Visual Solutions UsingDirect Observation. Improve yourobservation skills. Look through maga-zines for large photographs of heads.Look for adults, children, and babies.Remember that a head is not flat, andwhen it is turned, the central axis movesand curves around the shape of the head.You can always find the axis because itgoes through the center of the nose, lips,and between the eyes. Draw the centralaxis and the three horizontal dividinglines on each face.What are the propor-tional differences among the faces ofadults, children, and infants?

Computer Option. Gather some pic-tures of the faces of adults, children, andbabies. Notice that facial proportionschange with age. Use the drawing tools ofyour choice to draw a human face usingaverage facial proportions. Save yourwork. Use the Selection tool and theCopy and Paste options to duplicate thefirst face you drew.To experiment withthe size of facial features, use the Selectiontool to select the features of the face butnot the outline of the head itself. Use theResize option to create the correct fea-ture size for a young child. Save yourwork. Reduce the size even more to cre-ate the correct feature size for an infant.The features need to be small and in thelower third of its face. If possible, save allthree faces on the same screen. Finally,compare the three faces you have created.

� FIGURE 10.18 Even though Bonnard hasflattened and simplified this work, the differences inthe proportions between the profile of the fatherand the infant are easily measured. The skull of theinfant is very large, and the baby’s features seem tobe squeezed down into the lower part of the head.

Pierre Bonnard. Family Scene. From an album of L’EstampeOriginale. 1893. Color lithograph on heavy cream wovepaper. 31 � 17.8 cm (121�4 � 7�). The MetropolitanMuseum of Art, New York, New York. Rogers Fund, 1922.(22.82.1-3). © Artists Rights Society (ARS), NewYork/ADAGP, Paris.

both the front and two profile views of awoman’s head.

Notice that the facial proportions ofinfants are different, as shown in theprint by Bonnard (Figure 10.18).

LESSON 3 How Artists Use Proportion and Distortion 267

Many artists use correct proportions in their work. They want everyviewer to recognize the person, place, or thing being shown. These

artists use correct proportion to create illusions of reality. This ability to showobjects as though they were real seems magical to many viewers. Other artistschoose exaggeration and distortion to create works with unusual expressivequalities.

Realistic ProportionDuring the Renaissance in Italy, there

was a renewed interest in art and litera-ture. Ancient Greek and Roman sculp-tures were discovered, and artists wereinspired to create works with the realis-tic proportions of the ancient masters. Tobetter understand the human body, theartists Leonardo da Vinci and Michelan-gelo Buonarroti dissected cadavers insecret because dissection was illegal atthat time.

Michelangelo’s statue of David is anoutstanding example of Renaissance pro-portional accuracy. The artist was askedto create a bigger than life size figure ofDavid (Figure 10.19) for the façade ofthe Cathedral in Florence. When it wasfinished, the people decided that it wastoo important to be placed high up onthe cathedral. Instead, it was placed inthe main square and became a symbol of the city of Florence.

How Artists Use Proportion and Distortion

LESSON 3

Vocabulary

exaggerationdistortion

� FIGURE 10.19 One unusual feature of Michelangelo’s David isthe fiery intensity of the young man’s facial expression. He is staringat an enemy, the giant Goliath. What do you think David is thinking?

Michelangelo. David (detail). 1501–1504. Marble. Galleria dell’ Accademia,Florence, Italy.


Before the invention of photography,artists were hired to paint portraits torecord accurate information about realpeople (Figure 10.20). A contemporaryAmerican artist, Marisol, painted in thePop style in the 1960s. In Figure 10.21,she has used an unusual combination ofmaterials, yet she still uses accurate pro-portions for all of the figures.

� FIGURE 10.21 This mixed-media work is based on aphotograph that Marisol found among waste papers nearher studio. She uses realistic painting on the flat surfaces ofrectangular solids and recycled doors, and combines it withcarved wooden forms to create a realistic portrait of theunknown family. Notice the different accurate proportionsin this work. Use a ruler and you will see that the head-to-body ratio is appropriate for each figure.

Marisol. The Family. 1962. Painted wood and other materials in threesections. 209.6 � 166.4 � 39.4 cm (821�2 � 651�2 � 151�2�).Collection, Museum of Modern Art, New York, New York. AdvisoryCommittee Fund. © Marisol Escobar/Licensed by VAGA, New York, NY.

� FIGURE 10.20 Vigée-Lebrun painted thiswealthy princess without indications of her materialwealth so that she could emphasize her subject’sbeauty. Do the facial and body proportions of theprincess seem realistic?

Marie-Louise-Élisabeth Vigée-Lebrun. Portrait of PrincessBelozersky. 1798. Oil on canvas. 81.3 � 66.7 cm (32 �261�4�). National Museum of Women in the Arts,Washington, D.C.

Exaggeration and DistortionSome artists use exaggeration and

distortion rather than realistic propor-tion to convey their ideas and feelings.Exaggeration and distortion are devi-ations from expected, normal proportions.They are powerful means of expression.Artists can lengthen, enlarge, bend,warp, twist, or deform parts or all of thehuman body. By making these changes,they can show moods and feelings thatare easily understood by viewers. Theexaggeration used by the artist in Figure 10.22 lets us know how thewoman feels.


In the past, movie stars of the silentscreen had to exaggerate facial expres-sions and body language to conveymeaning without words. If you haveever seen an old silent movie, you haveprobably laughed at the exaggerated eye-lid movements used to express meaning.

It takes study and skill to use exagger-ation and distortion effectively. Beforean artist can distort a person or anobject, he or she must study perceptiondrawing and anatomy of the human fig-ure. It takes knowledge to know whatto exaggerate and how to distort imageseffectively.

In Single Family Blues (Figure 10.23),Twiggs has used exaggeration to expressthe feeling of “the blues” that engulf thisfamily. Notice that the hand is twice the size of the child’s blue head or themother’s blue-purple, or violet, face. Thisdistortion allows the viewer to see howdominant “the blues” are in this family.

� FIGURE 10.22The proud anxiety ofthe mother is expressedthrough the exaggeratedstretch of her arms andbody. She encouragesher daughter to walk,yet she is ready to catchher if she falls.

Napachie Pootoogook. MyDaughter’s First Steps. 1990.Lithograph. 55.8 � 85.8 cm(22 � 333�4"). Permissioncourtesy of the West BaffinEskimo Co-operative Limited.

� FIGURE 10.23 Twiggs uses exaggeration to emphasize the handplaying the blues for this family.

Leo Twiggs. Single Family Blues. 1996. Batik on cotton. 26.7 � 34.3 cm (101�2 �131�2"). Courtesy of the artist.


Pablo Picasso (pah-bloh pee-cah-so) was born in Malaga, Spain, in 1881.

One day his father, a painter and teacher, came home to a surprise. His son had

finished a portrait. After examining the work, Pablo’s father gave the boy all his

art materials. So great was Picasso’s work that his father vowed never to paint

again. Picasso was just eight years old.

He went to Paris in 1904. There he met other artists and writers. The creative

climate encouraged him to develop a new style, which he called Cubism. Com-

bining his appreciation of African art with his interest in geometrical forms, he

created a unique and innovative form. His aim was to shock viewers into visual

awareness. His intensity drove him to experiment with all media, discovering new

forms and new ideas. He painted Cubist works as well as realistic representations

of people. He also created prints and collages throughout his long and full life.

MEET THE ARTIST

PABLOPICASSO

Spanish 1881–1973

� FIGURE 10.24 Picasso exaggerates the thinnessof this old man, elongates his limbs, and places him inan impossibly angular position to create a paintingthat expresses sympathy for his condition. How doesthe contrast between the thin, angular man painted inblue and the warm brown, rounded guitar affect themeaning of this work?

Pablo Picasso. The Old Guitarist. 1903. Oil on panel. 122.9 �82.6 cm (483�8 � 321�2�). The Art Institute of Chicago, Chicago,Illinois. Helen Birch Bartlett Memorial Collection. © 2003Estate of Pablo Picasso/Artists Rights Society (ARS), New York.

Picasso was also a master of distortingproportion to express an idea or feeling.The works he painted during the earlytwentieth century are known as his“Blue Period.” During this time hepainted poor and tragic people. Despitethe sorrowful condition of the figures,

there seems to be a sense of optimism inthe works. In The Old Guitarist (Figure10.24), the grotesquely thin old manseems unaware of his condition. Hishead is bent toward the instrument as ifnothing matters but the beautiful soundof his music.

that stand out as masterpieces of Russ-ian literature. A message in Russian, “ToGogol from Chagall,” is incorporatedinto the design.

Artists can create feelings of great sta-bility and calm by placing a small head ona large body. A monumental, or large andimposing, quality results. The monumen-tal quality of Gaston Lachaise’s WalkingWoman (Figure 10.26 on page 272) iscreated through exaggerated proportionsrather than through large scale.


� FIGURE 10.25 This watercolor represents a design for a backdrop commissioned by a Moscow theatre.The backdrop was used as scenery for a play by the famous Russian nineteenth-century writer Gogol.

Marc Chagall. Homage to Gogol. 1917. Watercolor on paper. 39.4 � 50.2 cm (151�2 � 193�4�). Museum of Modern Art, New York,New York. Acquired through the Lillie P. Bliss Bequest. Licensed by SCALA/Art Resource, NY. © 2003 Artists Rights Society (ARS),New York/ADAGP, Paris.

In his painting Homage to Gogol (Fig-ure 10.25), Chagall used exaggerationand distortion to emphasize his love ofthe theatre. Some say that the hugeblack figure who is stretched andtwisted into an exaggerated bow is Cha-gall himself. He is holding a laurelwreath in one hand and balancing achurch on his foot while bowing toGogol. Chagall greatly admired NikolayVasilyevich Gogol, a nineteenth-centuryauthor of plays, short stories, and novels


Another use of exaggeration can beseen in the features of a mask. Maskshave been used in all societies, fromearly primitive tribes to our moderncomputer age (Figure 10.27). A maskallows a person to hide his or her realself and become someone, or some-thing, else.

Masks are used in many cultures aspart of religious ceremonies and rituals.In many cases the features of the maskare exaggerated for expressive purposes.Each culture has specific traditions andprocedures that are followed for makingand using masks. Sometimes the maskappears to the person in a dream. Some-times the mask is part of a cultural tradi-tion. In most cases the mask is intendedto aid efforts in communicating with thespirit world.

Cartoons are another way in whichexaggeration can be used. Editorial car-toonists use this technique to make cari-catures of famous people. (See page 284for more about how cartoonists useexaggeration.) The caricatures empha-size unusual facial features. Similarly,characters in comic strips are oftenmade by using proportions that arelarger than life. The most distortedcomic-strip characters are often the funniest ones.

� FIGURE 10.26 This sculpture is only 191�4 inches (48.8 cm) high andyet it has a monumental quality because Lachaise has made the head smallin comparison to the body.

Gaston Lachaise. Walking Woman. 1922. Bronze. 48.8 � 26.9 � 18.9 cm (191�4 � 105�8 �71�2�). Hirshhorn Museum and Sculpture Garden, Smithsonian Institution, Washington,D.C. Gift of Joseph H. Hirshhorn, 1966.



1. How do exaggeration and distortionaffect proportion?

2. Why do artists use distortion?3. How can artists create monumental

qualities without using a large scale?4. Compare and contrast the proportion

of the heads in Figure 10.19 on page267 and Figure 10. 26 on page 272.

� FIGURE 10.27 Imagine sitting in the darkaround a fire when a mysterious figure jumps out ofthe dark into the dim flickering light wearing one ofthese masks. How would you feel? How doesexaggeration and distortion affect the expressivequalities of these masks?

(right) George Walkus. Secret Society Mask. (Four HeadedCannibal Spirit) 1938. Wood; cedar bark, shredded; string.53.3 � 129.5 cm (21 � 51�). Denver Art Museum, Denver, Colorado.

(bottom right) New Ireland, South Pacific Islands. Mask. c. 1920. Wood, paint, fiber, seashells. Height: 38.1 cm (15�).Milwaukee Public Museum, Milwaukee, Wisconsin.

DistortingProportions

Applying Your Skills. Cut two ovalsabout 9 inches long from any color ofconstruction paper. Using parts cut frommagazines, create one face using accurateproportions. On the second oval, create adistorted face.

Computer Option. Use the drawingtools of your choice to draw a humanface using average facial proportions. Usethe Select tool and the Copy and Pasteoptions to make four or five copies of thehead and face on the same screen. Usethe Select tool to experiment with thewhole head and with individual facial fea-tures. Resize, Distort, Rotate, and Bendare some options that may prove usefulto you. If your software does not havethese options, draw the changes with thedrawing tools of your choice. Save yourwork. Compare the faces you have dis-torted and changed. How does the dis-tortion affect the way you would useeach face in a piece of artwork?

10–1

� FIGURE 10.28

George Bellows. Both Members of This Club. 1909. National Gallery of Art,Washington, D.C.

Historical and CulturalContext

In his painting Both Members of ThisClub (Figure 10.28), turn-of-the-twentieth-century American artistGeorge Bellows brings us ringside toview the action of a boxing match. Takea moment to study this work. Notice inparticular the straining muscles of thefighters. Observe the bloodied face ofthe boxer on the left. The viewer isalmost able to feel, as much as see, theimpact of the blows in this contest ofbrute strength.

One particularly important deviceworth noting is the artist’s use of theGolden Mean to organize the composi-tion. (See Figure 10.6, page 258.) Bybreaking up the two-dimensional spaceusing this classical mathematical for-mula, the composition is stabilized. Thefighters and spectators—both real and inthe painting—are locked in an intensemoment of time. Which member of theclub will break the clinch? Only timewill tell.

What You Will LearnYou will create a nonobjective tissue

paper collage, following the proportionsof the Golden Mean (see page 256). Youwill then make a contour drawing of astudent model in a classroom studio set-ting that includes furniture and objects.The drawing is intended to convey theatmosphere of an art classroom studio.You will unify the composition byadding acrylic glazes in a color schemerelated to the collage colors.

SUPPLIESSketchbook and pencil

Ruler

Large sheet of heavy drawing paper

Tissue paper, light to medium values

Diluted white school glue or matte medium adhesive

Black permanent felt-tip markers, thick and thin point

Tray or palette for color mixing

Acrylic paints and assorted brushes

STUDIOPROJECT The Golden Mean

and Mixed Media


Creating Members of the class are to take turns

modeling. Other students are to positionthe model and suggest different poses.Do several quick gesture drawings inyour sketchbook of various poses. Setaside the sketch you like best. Decide onthe mood your work will convey. Jotdown the names of colors that suggestthis mood.

Choose a horizontal orvertical format for your paper. Using aruler, divide your paper using the 1 to1.6 ratio of the Golden Mean. Decidewhere your figure will be placed. Makea light pencil mark at the focal point ofyour figure.

Gather sheets of tissuepaper according to your color scheme.Tear varying shapes and sizes of paper.Use these to create a composition thatleads the eye to the focal point. Overlapshapes and glue these down using mattemedium or diluted white glue that driesclear. (See Technique Tips Handbook,pages 440–441.)

When the glue has dried,transfer your sketch to the collage. Thecenter of your figure should be at thefocal point. Using a fine-tipped marker,reinforce the contour lines of your fig-ure as well as important details. Addelements of the environment, such asfurniture.

Select one of the colors inthe tissue paper collage. Using acrylicpaint, glaze over portions of the back-ground in order to define the figuresand unify the composition. Keep thepaint thin and transparent. Do not cover the entire surface. Vary the val-ues. There should be a balance betweenthe drawn and painted areas of thecomposition.

Step 4

Step 3

Step 2

Step 1

� DESCRIBE Tell what objects are depicted inyour work. Point to areas of your work thatare nonobjective.

� ANALYZE Explain and describe how youused the Golden Mean in your composition.Compare and contrast the use of color, pro-portion, and unity in your artwork.

� INTERPRET Does the composition create a mood that represents the art studio and themodel? Does the color scheme fit the moodyou were trying to create? Give your work atitle that sums up the expressive quality ofyour work.

� JUDGE Is there anything you would changeto make the work more successful? Which ofthe three aesthetic theories would you use tojudge your work?

Evaluating Your Work

� FIGURE 10.28A

Student work.

STUDIO PROJECT The Golden Mean and Mixed Media 275

10–2

Historical and CulturalContext

When you first look at Figure 10.29,you almost mistake the work for a pho-tograph. This work is an example of photorealism, art created with the preci-sion found in photographs. Note thatthe work was created in the late 1800s,just as photography was coming into itsown right.

Take a moment to study this painting.It is more than a simple portrait. It is atribute to a musician. You can tell fromthe symbols in the painting—whichinclude Apollo, the god of music, who isdepicted standing on a column. Thegolden lyre behind the main subject alsorepresents Apollo. What other objectscan you find that appear to have sym-bolic value?

What You Will LearnYou will paint a realistic self-portrait.

You will add symbolic images thatreflect aspects of your personality, inter-ests, culture, and/or dreams for thefuture. You will enhance the realisticquality of your work by using water-color and pen-and-ink techniques tocreate values and textures.

CreatingIn your sketchbook write a list of

words you would use to describe your-self, your personality, your interests,and so on. Choose the words that fit youbest, and think of symbols to representthose words. Be creative.


Soft eraser

Mirror

Hot press watercolor paper or heavy white paper

Masking tape

Drawing board

Watercolors, brushes, and water jars

Fine-line, nontoxic black ink pen

STUDIOPROJECT Symbolic

Self-Portrait


� FIGURE 10.29

Gustav Klimt. Portrait of Joseph Pembaur. 1890. Oil on canvas. 69 �55 cm (271�8 � 212�3�). © Erich Lessing/Art Resource, NY. TirolerLandesmuseum Ferdinandeum, Innsbruck, Austria.

Select three to five ideasfrom your list. Practice drawing thesymbols you have thought of, usingpen-and-ink shading techniques. (SeeTechnique Tips Handbook, page 429.)When drawing your symbolic objects,try to work from direct observation.

Using a mirror, practicedrawing self-portraits in your sketch-book in pencil. See pages 264–265 forspecific directions for drawing heads andfaces in correct proportions.

Begin planning a composi-tion that combines your portrait withthe symbols you have selected. Makesmall rough drawings in your sketch-book, trying different arrangements ofthe head and symbols. Think about thefocal point and the use of negative spacein your composition. Choose your bestrough sketch for your final work.

Tape a sheet of drawingpaper onto your drawing board. Drawthe composition you have selected. Fillthe page. Use a very light pencil linethat will not show through the water-colors. Draw your symbols.

Switching to watercolorsand brush, start painting your face.Continue using the mirror to help yousee the hues and values of your face.Start with the lightest colors first. Grad-ually add the darker colors. You willneed to work in layers, letting one layerdry before adding the next. Use value tomake your face as three-dimensional aspossible. You can always make a water-color area darker, but it is almost impos-sible to make it lighter.

Next, paint the symbols andbackground.

Once the paint has dried,add pen-and-ink details.

Step 7

Step 6

Step 5

Step 4

Step 3

Step 2

Step 1

� DESCRIBE What symbolic imagery did youuse? What does each symbol represent aboutyou? Does your work bear a likeness to you?

� ANALYZE Did you paint your portrait usingaccurate proportions? Did your use of water-color and pen and ink enhance the portrait?Did you include light and dark values to givethe face three dimensions? Does your facedominate the composition or do the symbolsdominate?

� INTERPRET What does your painting tellabout you? What do the symbols reveal?Give your painting a title that sums up whatyou were trying to express about yourself.

� JUDGE If you were to do this painting over,what changes would you make? Justify yourartistic decisions.


STUDIO PROJECT Symbolic Self-Portrait 277

� FIGURE 10.29A

Student work.

10–3Historical and CulturalContext

The early-twentieth-century artmovement known as Surrealism tookthe unreal and made it plausible. One of the masters of this movement wasSalvador Dali, who drew the unworldlycreatures in Figure 10.30. These fantas-tic elephants are relatively ordinarycompared to Dali’s other creations.Many of his works, rendered with pho-torealistic quality, present a nonsensicalworld where anything goes—where upis down, night is day, and so on.

One recent art development that issimilar in spirit to Surrealism is digitalfine art. It, too, draws on a world thatdefies the laws of nature, and whereanything is possible.

What You Will LearnUsing your imagination, you will cre-

ate a fantasy creature with exaggerationand distortion. You will combine differ-ent insect, animal, and human bodyparts to produce a new, imaginary crea-ture with the help of a paint or image-editing program. (See Digital Handbook,page 449). You will then create an envi-ronment in which to place this creature.


Magazines, clip art, or original photographs

Computer

Scanner

Paint or image-editing program

Graphics tablet, optional

Digital FantasyCreature

STUDIOPROJECT


� FIGURE 10.30

Salvador Dali. The Elephants (Design for the Opera La Dama Spagnola e ilCavaliere Romano). 1961. Indianapolis Museum of Art, Indianapolis,Indiana. © 2003 Salvador Dali, Gala-Salvador Dali Foundation/Artists Rights Society (ARS), New York.

CreatingStart by drawing an image of a person

or an animal in your sketchbook. Con-sult nature magazines or other artresources for ideas. Experiment withexaggerating or distorting various physi-cal features such as arms and legs. Trylengthening, shortening, thickening,thinning, and multiplying body parts.Find unexpected combinations of shapes.

Use a paint or image-editingprogram to recreate the insect, animal,or human figure. Use the software’sdrawing tools or a graphics tablet (seeDigital Handbook, page 448), if one isavailable. If you like, combine yourdrawing or painting with scannedimages from magazines, clip art, or original photographs.

Experiment with copyingand pasting different parts of your crea-ture. Use the program’s tools to stretch,shrink, or otherwise alter these parts.Try changing and distorting the propor-tions. Save your work frequently.

If filters or special effectsmenus and tools are available, continueto alter your image. Add contrastingtextures, shapes, and colors. Zoom inoccasionally to clean up any rough lines,stray pixels, or other mistakes.

Once you are satisfied withthe imaginary creature, create a surpris-ing and illogical background for it. Onceagain, choose the tools available in thesoftware program to add interest to thesetting you design. If your softwareoffers Layering, create multiple layers.You can create the illusion of depth andatmospheric perspective using layers.

After you have saved yourfinal composition, print it. Prepare yourfinal copy for display.

Step 5

Step 4

Step 3

Step 2

Step 1

� DESCRIBE What animal, insect, or humanpart(s) did you use to create your imaginaryfigure? Identify the features you have dis-torted and exaggerated. Describe the thingsyou have added to create an illogical back-ground. List, in order, the specific hardwareand software you used.

� ANALYZE Explain how you used exaggera-tion and distortion to create your creature.Describe the colors and textures you used toenhance the creature and background.

� INTERPRET Describe the mood, theme, or idea you have created. Is your creaturefunny? Frightening? Give your work adescriptive title that sums up the feeling ormood it conveys.

� JUDGE Have you successfully combined,exaggerated, and distorted the features ofyour creature to emphasize an idea or mood?Is there anything you would change? Whataesthetic theory would you use to judge thisartwork?

� FIGURE 10.30A

Student work.


DIGITAL STUDIO PROJECT Digital Fantasy Creature 279

STUDENTART PORTFOLIO

You wouldn’t think twice if a car drove by. You might

do a double take, however, if the car were 90 feet long.

Proportion in art, as in life, can command your attention.

As you examine the student artworks on these pages:

Compare and contrast them in terms of their use of the principle ofproportion.

Analyze the works, forming precise conclusions about the type of proportion used.

Analyze the works, forming precise conclusions about the artist’s intent.

Proportion


Activity 10.31 Form and proportion.Notice how this artist has used circular formsof varying sizes. Compare and contrast theforms in this art object. Which ones receivethe most emphasis?

� FIGURE 10.31

Student work. Untitled. Cabinet hinge, lock washers, rubberdisks, and wire connectors on a satin cord, spray-painted black.88.9 x 101.6 mm (31�2 � 4").

Activity 10.32 Golden Mean.Compare and contrast this artwork with Figure 9.19 on page 239. Analyzeeach artist’s use of the proportions of the Golden Mean.

� FIGURE 10.32

Student work. Red and Blue Figure Study. Monoprint.22.9 � 304.8 mm (9 � 12").

To view more student artworksvisit the Glencoe Student ArtGallery at art.glencoe.com.

ART

For Your PortfolioAnalyze Personal Artworks. As you build your artportfolio, compare and contrast the use of proportionin your artworks. Make sure to include some humanfigure drawings.These will reflect your understandingof the Golden Mean. Be sure to attach notes that detailthe principles used in an artwork’s design. Also, identifythe art elements that these principles organize.

Evaluate the portfoliosof other artists and keepthese notes in your artjournal.Work with yourteacher to gather a collec-tion of artists’ portfolios.Select and analyze theportfolios to form conclu-sions about formal quali-ties, historical and culturalcontexts, intents, andmeanings. Add sketches toyour evaluations to illus-trate your conclusions.

STUDENT ART PORTFOLIO Proportion 281

� FIGURE 10.33

Student work. Portions of Me. Pen and ink, watercolor.457.2 � 457.2 mm (18 � 18").

Activity 10.34 Exaggeration and distortion.Evaluate this sculpture in terms of the artist’sprobable intent. Do you think the student artist’sgoal was to achieve realism? Explain.

� FIGURE 10.34

Student work. All Alone in the Moonlight. Clay,acrylic, mixed media. 127 x 177.8 x 76.2 mm(5 � 7 � 3").

Activity 10.33 Scale. Analyze this student artwork,noting its actual size. Compare the scale of these facialfeatures with those of a life-size face. Form conclusionsabout the artist’s intent.

� FIGURE 10.35

Marc Chagall. The Green Violinist. 1923–24. Oil on canvas. 198 � 108.6 cm (78 �423�4�). The Solomon R. Guggenheim Museum, New York, New York. Gift, SolomonR. Guggenheim, 1937. © 2003 Artists Rights Society (ARS), New York/ADAGP, Paris.


1 DESCRIBE What do you see?List all the information found in the credit line.

Describe the main figure in this painting. Do the man’sfeet appear to be touching the ground? Explain.

Can you find any other figures or objects in the work?Describe everything that you see.

2 ANALYZE How is this work organized?This is a clue-collecting step about the elements andprinciples of art.

Compare the artist’s use of bright colors for someobjects and pale colors for others. Explain why he hasused the element of color in this fashion.

Compare and contrast the artist’s use of color and formand the art principle of proportion.

3 INTERPRET What message does this artworkcommunicate to you?Combine the clues you have collected to form a creative interpretation of the work.

Notice that the violinist cradles his violin almost asthough it were a baby. What does this tell you abouthis feelings toward the violin? About the music that hemakes?

Does everyone in the painting seem to hear the music?Explain.

4 JUDGE What do you think of the work?Decide if this is a successful work of art.

After analyzing this work, form a conclusion about theartist’s intent. Did he intend to create a lifelike work ofart? Which aesthetic theory would be most applicableto this work? Explain your answer.

Marc Chagall was born in asmall town in Russia to a poor,Jewish family. He studied art in St. Petersburg, and moved toParis upon graduation. In 1914,he returned to Russia for a visitbut was unable to leave whenWorld War I broke out. In 1918,he was appointed Commissar ofArt. After the war, Chagallreturned to Paris. His subjectmatter ranges from personalexperiences and folklore to Bibli-cal stories. In addition to hispainting, he is noted for hismosaics and stained-glass win-dows. Some of his murals hang inthe Metropolitan Opera Housein New York City.

Critiquing the Artwork

Art Criticism in Action 283

Marc Chagall (1887–1985)

Political cartoonists drawthe world as they see it—just off center.

Q. What is a political cartoon?

A. It’s a drawing that comments—often in a humorous way—on people, events, and ideas inthe news. Political cartoonists have to amuse their readers and addresscomplicated issues using just ink and a few words.

Q. How do political cartoonists create their humor?A. One way is by exaggerating the physical features or proportions

of the people they draw—a technique called caricature. For example, apolitical cartoonist may take the symbols of the American political parties,the donkey and the elephant, and draw them the size of a person, complete with coat and tie. Or a cartoonist may poke fun at politicians by shrinking them down to the size of a baby.

Q. How does a political cartoonist get started?A. Signe Wilkinson draws cartoons for the Philadelphia Daily News

and other newspapers. Her career began with doodling—somethingshe started doing as a child. Her first job was reporting for a news-paper in Pennsylvania. Wilkinson began drawing the people shewas supposed to be writing about. Back in the newsroom, shefine-tuned her doodles and convinced some editors to pub-lish her work. “I realized that I liked drawing more than writing,” Wilkinson says. She also realized that cartooningcombined her interests in art and politics. “[We] take a topic, likegun control, and express how we feel through our drawings.”

TIME to Connect

Using your school’s media center or the Internet, find political cartoonsthat were published during one of these significant points in American his-tory:World War II, the Vietnam War, and the corporate scandals of 2002.

• What was the significance or importance of each of the events and/or peopleshown in the cartoons? Where were they originally shown? What are thepoints of view of the cartoonists regarding the subject, event, or politician?

• As a class, create a display that shows copies of the cartoons, organizing themby subject matter and time period. Discuss the cartoonists’ points of view.

Signe Wilkinson takes on themedical profession and healthinsurance companies in thispolitical cartoon.What examplesof exaggeration can you find inher drawing?


©2003, THE WASHINGTON POST WRITERS GROUP. REPRINTED WITH PERMISSION.

Self-portrait of Wilkinsonat work.

SIG

NE

WIL

KIN

SO

N

Chapter 10 Review 285

Use the Performing ArtsHandbook on page 422 todiscover how Eugene Friesenexplores the elements of exaggeration anddistortion of human proportions throughthe use of masks in his performance of“Cello Man”.

Building Vocabulary

On a separate sheet of paper, write the termthat best matches each definition given below.

1. The principle of art concerned with the sizerelationship of one part to another.

2. A line divided into two parts so that thesmaller line has the same proportion, orratio, to the larger line as the larger linehas to the whole line.

3. Size as measured against a standard reference.

4. Figures arranged in a work of art so thatscale indicates importance.

5. To shorten an object to make it look as if it extends backward into space.

6. Deviations from expected, normal proportions.

Reviewing Art Facts

Answer the following questions using com-plete sentences.

7. What is the Golden Mean ratio?

8. Explain the difference between scale andproportion.

9. What was the name for the geometric formthat had sides matching the ratio of theGolden Mean?

10. What are the two kinds of scale in art?

11. What unit is usually used to define theproportions of any individual figure?

Thinking Critically About Art

12. Extend. Do some library research to deter-mine how hierarchical proportions havebeen used in the art of different cultures.Photocopy examples to show and reportyour findings to the class.

Fashion designersneed to understandthe rules of humanbody proportions.

These artists illustrate their designs with figuredrawings. Not only must the illustrationsreflect realistic human proportions but alsotheir clothing must fit the human body.Visitart.glencoe.com to compare and contrastcareer opportunities in art.

ART

13. Compare and Contrast. Siqueiros’s paint-ing, Self-Portrait (Figure 10.14, page 264)uses a distortion called foreshortening to create a symbolic proportion. The Oba figure(Figure 10.10, page 262) also uses symbolicproportion. Compare the two works. List thesimilarities and differences. Explain what thedistortion conveys in each artwork.

14. Historical/Cultural Heritage. Review theMeet the Artist feature on Pablo Picasso onpage 270. Picasso both initiated and fol-lowed many art trends throughout his longcareer. Compare and contrast Figure 10.24on page 270 with Figure 6.26 on page 154.These artworks were created within a ten-year span of each other. Identify the generaltrend that both paintings reflect in their useof color and proportion.

Linking to thePerforming Arts

CHAPTER 10 REVIEW

254 chapter 10 proportion - janessa friesen · 254 chapter 10 proportion figure 10.1 this painting...

Documents