İslamic art and geometry design

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The Metropolitan Museum of

Islamic Art and

Geometric Des

ACTIVITIES FOR LEARNING


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Copyright 2004 by The Metropolitan Museum of Art, New Yorkublished by The Metropolitan Museum of Art, New York

his resource for educators is made possible byhe Mary and James G. Wallach Foundation.

ducation, The Metropolitan Museum of Art

roject Manager: Catherine Fukushimaenior Managing Editor: Merantine Hensenior Publishing and Creative Manager: Masha Turchinskylustrations and design by Tomoko Nakano

Color separations and printing byUnion Hill Printing Co., Inc., Ridgefield, New Jersey

All photographs of works in the Museums collection are byhe Photograph Studio of The Metropolitan Museum of Artxcept for the following: nos. 14 and 20 by Schecter Lee;os. 17 and 18 by Malcom Varon, N.Y.C.

SBN 1-58839-084-5 (The Metropolitan Museum of Art)SBN 1-300-10343-3 (Yale University Press)brary of Congress Control Number: 2003110847

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Contents

Introduction and How to Use These Materials

Introduction to Geometric Design in Islamic Art

Selected Works of Art in The Metropolitan Museum of Art

Pattern-Making Activities

Resources and Glossary


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Acknowledgments

We are extremely grateful to the Mary and

James G. Wallach Foundation, whose grant

enabled us to publish Islamic Art and Geometric

Design and make it available to the many math,

humanities, and science teachers who have

requested it for use in their classrooms.

The creative vision and leadership of Jane

Normanan educator at the Metropolitan Museum

for twenty-five yearsare behind the originalversion of this publication. Over the year s, other

educators at the Museum, including Evan Levy,

Betty Rout, Alice Schwarz, and Lena Sawyer,

refined and expanded upon the initial concepts.

We are indebted to Stefano Carboni, curator, and

Qamar Adamjee, research assistant, both of the

Department of Islamic Art, who revised the

Introduction to Geometric Design in Islamic Art

and ensured that the information about the

selected works in the Museum represents the latest

scholarship. Educators Nicholas Ruocco and

Deborah Howes offered insight and

encouragement. Emily Roth and Naomi Niles

refined the bibliography. Catherine Fukushima

shepherded this project, together with Merantine

Hens, who coordinated the many steps of editing.

Philomena Mariani edited the manuscript and

Tonia Payne provided meticulous proofreading.

Sue Koch of the Design Department provided

valuable guidance. Masha Turchinsky art directed

and managed the various aspects of production,

working closely with Tomoko Nakano, who created

the effective illustrations and the handsome design.

Kent Lydecker

Associate Director for Education

Preface

In 1976, Jane Normanwith help from Harry

Bixler, Stef Stahl, and Margit Echolswrote

The Mathematics of Islamic Art, a groundbreaking

Museum publication responding to the needs

of math teachers eager to use the Museums

resources in their classrooms. It became one of the

Mets most popular educational publications and

has long since been out of print. This new iteration,

Islamic Art and Geometric Design, which includes

current scholarship on Islamic art as well asexpanded activities developed in Museum

workshops, remains indebted to Jane Normans

work. We therefore dedicate this publication with

gratitude, affection, and admiration to Jane, whose

inceptive vision and passion for this project has

inspired all that has followed.

Foreword

Surface patterns on works of art created in the

Islamic world have been prized for centuries for

their beauty, refinement, harmony, intricacy, and

complexity. Fine examples of Islamic art, from the

seventh to the nineteenth century, can be seen in the

Metropolitan Museums collection. This publication

features a selection of those objects in which

geometric patterns predominate. By using these

materials teachers will be able to show their students

how Islamic artists applied their imagination to anunderlying geometric framework to create the

patterns in these outstanding works of art. Students

will also learn the principles of geometric patterns

and be able to create their own. We hope that these

activities will spark in your students a life-long

interest in art and design.

We are fortunate indeed that these educational

materials are supported by the Mary and

James G. Wallach Foundation. Their contribution

underscores their high commitment to art, to

students, and to teachers. We are deeply grateful

for their generosity.

Philippe de Montebello

Director

Kent Lydecker

Associate Director for Education


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of the objects. Let your students know that thewill have the opportunity to create many ofthese patterns themselves.

Lead your students through the pattern-making activities. You may chose to do one,some, or all of them. A set of overheadtransparencies of the activity grids in thisbooklet is provided for your convenience.

After the class has completed the activities,

return to the slides for a more in-depthdiscussion of the patterns and effects of thedesigns. Help the students find patterns similto the ones they created themselves.

We hope that this publication will inspirenew projects that combine visual art andmathematical and geometric concepts.

A series of activities follow. Working onlywith a straightedge and a compass, s tudentswill discover how to create many of thegeometric shapes and patterns that Islamicartists preferred. They will also learn howthe underlying grid structure serves as thefoundation upon which these patterns maybe infinitely repeated.

The humanities teacher will find that close studyof works of art will lead students to a greater

understanding of artistic and cultural concepts.Math teachers can use the activities to reinforcegeometric principles. Art teachers will find thatstudents become absorbed in the creation oftheir own geometric patterns. And scienceteachers will recognize that many underlyingprinciples of these patterns have corollariesin the natural world.

The following suggestions are offered asguidelines when using these materials:

Become thoroughly familiar with the materialsbefore you use them with your students.

Use the slides as a starting point. As studentsview the visual materials, they will becomeinterested in the designs and curious about howthey were created.

Explain the traditions of Islamic art to yourstudents. A brief introduction to Islamic art andmore detailed information about the individualworks of art, including title, purpose, origin,and materials, are provided.

When viewing the slides, call attention tothe intricate patterns used in the decoration

Introduction

Works of art can be stimulating starting pointsfor interdisciplinary investigations leadingstudents to explorations of history, socialstudies, geography, and culture. Lesscommonly, but no less intriguing, art may bea stimulus for exploring concepts in math andgeometry. This resource provides the means forteaching about the history and providing anintroduction to Islamic art while learning about

the variety of geometric patterns employed byartists to embellish a wide range of works ofart, including textiles, ceramics, metalwork,architectural elements, and manuscripts.Through the activities, students will learn thedesign principles and techniques by whichthe artists created these beautiful andintricate patterns.

How to Use These Materials

These materials may be used by a singleteacher, or a team of teachers maycollaborate, each working in his or her owndiscipline. The activities may be adaptedto all levels of instruction.

We begin with an introduction to geometricpatterns in Islamic art. Slides of works from theMetropolitan Museums collection are includedto show the variety and originality of thesedesigns. A brief overview of Islamic art andindividual object descriptions prepare theteacher to lead a discussion of the slides. Fora chronological survey of Islamic art, teachersmay refer to the Timeline of Art Historyatwww.metmuseum.org/toah.


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Introduction to Geometric Design inIslamic Art

The principles and teachings of Islam as away of life, a religious code, and a legalsystem were promulgated by Muhammad(ca. 570632 A.D.), an Arab merchant fromMecca. These teachings were revealed tohim over a period of many years beginningin 610 and were subsequently codified in thetext known as the Quran. The word of God,

as set out in the Quran and handed down inthe sayings of Muhammad (known as hadith,or Traditions), forms the core of the religion.

The primary premise of the Islamic faith ismonotheism, a renunciation of all deities exceptone, Allah, who alone is the creator, sustainer,and destroyer of life. Islam is Arabic forsubmission, here to the single entity of Allah.The recognition of Muhammad as Allahs lastprophet, a prophet like Abraham, Moses,

Jesus, and the others that preceded Muhammad,is also a key element of the belief.

Neither the Quran nor the Traditions containspecific mandates against figural representa-tion in art. However, both sources take a firmstance against idolatry and the worship ofimages. These precepts were interpreted strictlyby early Islamic religious leaders and exegetesas an injunction against the depiction of humanor animal figures, although extant examples ofarchitectural decoration, objects in all media,and illustrated manuscripts belie that stricture.Four types of ornamentation can be found inIslamic art: calligraphy, figural forms (humanand animal), vegetal motifs, and geometricpatterns. These patterns, either singly or

combined, adorn all types of surfaces, formingintricate and complex arrangements.

While geometric ornamentation may havereached a pinnacle in the Islamic world,sources for the basic shapes and intricatepatterns already existed in late antiquity in theByzantine and Sasanian empires. Islamic artistsappropriated key elements from the classicaltradition, then elaborated upon them to inventa new form of decoration that stressed the

importance of unity, logic, and order. Essentialto this unique style were the contributionsmade by Islamic mathematicians, astronomers,and other scientists, whose ideas and technicaladvances are indirectly reflected in theartistic tradition.

The basic instruments for constructing geometricdesigns were a compass and ruler. The circlebecame the foundation for Islamic pattern, inpart a consequence of refinements made tothe compass by Arabic astronomers andcartographers. The circle is often an organizingelement underlying vegetal designs; it plays animportant role in calligraphy, which the Arabsdefined as the geometry of the line; and itstructures all the complex Islamic patterns usinggeometric shapes. These patterns have threebasic characteristics:

1. They are made up of a small number ofrepeated geometric elements. The simple formsof the circle, square, and straight line are thebasis of the patterns. These elements arecombined, duplicated, interlaced, andarranged in intricate combinations. Mostpatterns are typically based on one of twotypes of gridone composed of equilateral

triangles, the other of squares. A third typeof grid, composed of hexagons, is a variationon the triangular schema. The mathematicalterm for these grids is regular tessellation(deriving from Latin tesserae, i.e., pieces ofmosaic), in which one regular polygon isrepeated to tile the plane.

2. They are two-dimensional. Islamic designsoften have a background and foregroundpattern. The placement of pattern upon pattern

serves to flatten the space, and there is noattempt to create depth. Vegetal patterns aremay be set against a contrasting background inwhich the plantlike forms interlace, weavingover and under in a way that emphasizes theforeground decoration. In other instances, thebackground is replaced by a contrast betweenlight and shade. Sometimes it is impossibleto distinguish between foreground andbackground. Some geometric designs arecreated by fitting all the polygonal shapestogether like the pieces of a puzzle, l eavingno gaps and, therefore, requiring no spatialinterplay between foreground and background.The mathematical term for this type ofconstruction is tessellation. The conception ofspace in Islamic art is completely different fromWestern models, which usually adopt a linearperspective and divide the picture space intoforeground, middle ground, and background.Artists of the Islamic world were largelyuninterested in linear perspective. Of thevarious styles of Islamic art, it was in Persianpainting that a type of three-dimensional spacewas used in which figures could interact, butthis space presented multiple viewpoints andsimultaneously featured birds-eye andworms-eye views.

3. They are not designed to fit within a frameGeometric ornamentation in Islamic art sugga remarkable degree of freedom. The complarrangements and combinations of elementsare infinitely expandable; the framesurrounding a pattern appears to be arbitrarand the basic arrangement sometimes provida unit from which the rest of the design can bboth predicted and projected.


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Textile fragment, 14th15th century; Nasrid periodSpainSilk, compound weave; 40 3/8 x 14 3/4 in. (102.6 x 37.5 cm)Fletcher Fund, 1929 (29.22)

The patterns on this textile fragment recall the decorationon the tiles and painted stucco adorning the walls of theAlhambra in Granada, the capital of the Nasrids, the lastruling Islamic dynasty in Spain. The various forms ofIslamic ornament are presented on this textile withbrilliant contrasting colors to create a sense of animationand balance. The main repetitive motif in the geometricbands consists of an eight-pointed star formed by twooverlapping squares. Vegetal patterns, knotted angularkuficscript, and cursive naskh script in the cartouchesabove and below the kuficbands enhance the overallgeometric effect of the design.

Openwork screen (jali), ca. 1610; Mughal periodIndia, probably AgraMarble; 48 1/8 x 16 1/2 in. (122.2 x 41.9 cm)Rogers Fund, 1984 (1984.193)

Pierced screens (jalis) of pink sandstone or whitemarble were widely used in Mughal India and fulfilledmany architectural functions, serving as windows, roomdividers, and railings. They allowed for the circulation ofair and provided shel ter from sunlight, but the geometricpatterns and their projected shadows also producedaesthetic effects.

Bowl, late 12th early 13th century; Seljuq periodIranMinaiware; composite body, opaque white glaze with gilding,overglaze painting; H. 3 11/16 in. (9.4 cm), diam. 7 3/8 in.(18.7 cm)Purchase, Rogers Fund, and Gift of The Schiff Foundation, 1957(57.36.4)

Minaiware was produced in Iran in the Seljuq period. Theceramics were noted for colorful figurative painting on a white

glaze. As one of the many conquering peoples who rode intothe Middle East from the Central Asian steppes, the ruling-class Turks are appropriately shown on horseback, theirAsiatic features easily distinguishable. The shape of thebowl is echoed in the design at its centera round sun,shown as a face, surrounded by the suns rays, and aroundthem, six regularly spaced figures representing the moonand five planets. This construction could easily lead to apattern of hexagons or six-pointed stars.

Leaf from a Quran manuscript, 13028; Ilkhanid periodIraq, BaghdadInk, gold, and colors on paper; 17 x 13 7/8 in. (43.2 x 35.2 cm)Rogers Fund, 1950 (50.12)

Traditions of bookmaking were well developed in Islam bythe eighth and ninth centuries, although such fully developedillumination as that on this leaf seems not to have becomewidespread until the eleventh centur y. Copies of the Quranreceived the greatest artistic attention and care. In thisexample, which represents the right side of a double-pagecomposition, many designs cover the entire surface of the page.In the center of the page lies a richly designed square decoratedwith complex geometric shapes and foliage designs. Aboveand below the square are two narrow rectangles decoratedwith calligraphic words set over leaves and vines. Over theentire space, carefully fitted into the geometric design, is a

pattern of leaves and flowers in diverse colors. Above andbelow the square are two narrow rectangles, which completethe design of the page. This sumptuous gold frontispiece usesa pattern of eight-pointed stars.

Laila and Majnun at School: Miniature from theKhamseh of Nizami, folio 129a16th century; Safavid periodIranInk, colors, and gold on paper; 7 1/2 x 4 3/4 in. (19 x 12 cm)Gift of Alexander Smith Cochran, 1913 (13.228.7)

Manuscript pages would have been executed in two stages.First the calligrapher would write the portion of the story to beillustrated, then the painter would compose pictures in the spaceleft by the calligrapher. Persian painters loved to dep ict thescene from Nizamis immortal romance, where Laila and Majnunas children attend the same school. These paintings give us afascinating glimpse of the goings-on in a classroom.

Laila and Majnun at School: Miniature from theKhamseh of Nizami, folio 129a(detail of slide 17)

This detail shows the painters ability to combine differentpatterns to create a surface richness that contradicts thesense of space suggested by certain lines of perspective.Note the two designs using six-pointed stars.

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Mihrab, 1354; post-Ilkhanid periodIran, attributed to IsfahanMosaic of monochrome-glaze tiles on composite body set onplaster; 11 ft. 3 in. x 7 ft. 6 in. (3.4 x 2.9 m)Harris Brisbane Dick Fund, 1939 (39.20)

The most important interior element in an Islamic religiousbuilding is the mihrab, a wall niche that indicates the directionof Mecca, toward which the faithful must face during the dailyprayers. This mihrabis from the Madrasa Imami, a religious schoolfounded in Isfahan in 1354. It is made of glazed earthenwarecut into small pieces and embedded in plaster. Three kinds ofIslamic designs can be found here vegetal, calligraphic, andgeometric. The calligraphic inscription in the back of the nichereads: The Prophet (on him be peace!) said the mosque isthe dwelling place of the pious. Calligraphy is the mostrevered art form in Islam because it conveys the word of God.

Note the way in which straight-lined geometric shapes havebeen made to fit the curved space. Observe the varied andcomplex decorative elements that cover every visible surfaceof the mihrab. All directly illustrate geometric, calligraphic,or plant forms.

Tombstone, 753 A.H. / 1352 A.D.IranLimestone; 32 3/4 x 21 3/4 in. (83.2 x 55.3 cm)Rogers Fund, 1935 (35.120)

This tombstone recalls a mihrabniche. A common decorativefeature seen on mosque arches, domes, and sometimes onmihrabs are the three-dimensional forms known as muqarnas,or stalactites. Students should try to determine how the patternof stalactites was formed. While the four main types of Islamicornament were often included in various combinations orall together on a single surface, in other instances, one ty peof decoration was made to conform to the specifications ofanother, here seen by the geometric application of calligraphy.The inscriptions on the tombstone inside the niche, in thediagonally set square above the niche, and on the innerband that frames the nicheare a perfect exampleof the technique of rendering square kuficcalligraphy.This style evolved during the medieval period for use on

architecture because the angular Arabic letters fit easilyinto architectural spaces and could be conformed to therectangu lar shapes within the overall structure.

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Pattern-Making Activit


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Introduction

Through these activities, students will discoverthe satisfaction that comes with the creationof designs through the use of two simpletoolsa compass and a straightedge. Bycreating patterns themselves, students willgain an understanding of geometric principlesof the underlying grids and methods used byIslamic artists.

Each activity lists the materials needed in a boxin the upper right corner and illustrates how todo the activity. Pages of this booklet providinggrids and the circle template may be photocopied

for use with your class. A set of overheadtransparencies of the activity grids in thisbooklet is provided for your convenience.

Students begin by making single circles witha compass. By using two different arrange-ments of circles, students will be able to createa variety of geometric forms, including rosettes,hexagons, and eight-pointed stars. The nextset of activities demonstrates how the twoarrangements of circles are used to createvarious grids. Using these grids, students cancreate an infinite variety of patterns. The finalactivity is a class project in which students cutand decorate six- and eight-pointed stars toform two of the most popular Islamicpatternsthe hexagon and the star-cross.

Seven Overlapping Circlespaper,straighcompamarker

1.Using a straightedge, drawa horizontal line near thecenter of the paper.

2. Make a circle with the compasspoint placed near the center ofthe line. Using the intersectionpoints as new compass points,draw a circle on either side ofthe first circle.

3. Add four more circles usingthe new points of intersectionas compass points. It isimportant that all circleshave the same radius.

Activity 1


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Finding Geometric Shapes within Circles

Hexagon

To make a hexagon, use astraightedge to join adjacentcircumference points on thecentral circle.

Rosette

The rosette divides thecentral circle into six equalparts and locates six equallyspaced points on itscircumferencea

result of all the circleshaving the same radius.

Two equilateral

triangles

To create two equilateraltriangles, join every secondpoint. Notice that these twotriangles form a six-pointedstar.

Activity 2straightedge, marker,three examples of theseven overlapping circlesdesign made in Activity 1

For examples see Fountain from Nur al-Din room (slide 4) andLaila and Majnun at School:Miniature from the Khamseh of Nizami(slides 18)

Using the seven overlapping circles design created in Activity 1, students will be able to find threepossible shapes: rosette, hexagon, and equilateral triangle. Use a marker to highight each shape.


For an example see Pair of doors (slide 9)

straightedge, peone rosette madearlier in this ac

Start with the rosette onthe opposite page.

Connect every other point ofthe rosette to produce asix-pointed star with overlappingtriangles and ahexagon inthe center.

Connect opposite corners ofthe hexagon within the star.Extend the lines to the edgeof the central circle to dividethe star into twelve equilateraltriangles. Erase the linesinside the central circle,leaving the circle and lineend points visible.

Connecting every fifth pointwill produce atwelve-pointed star.

1.

4.

2. 3.


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Activity 3

Creating Triangle and Hexagon Grids

straightedge, two differentcolored markers, tracingpaper, seven overlappingcircles grid (fig. 1)

Now you have the trianglegrid on the tracing paper.Using a different color ofmarker, mark the hexagongrid by highlighting theouter edge of six adjoiningtriangles, as shown.

On the seven overlappingcircles grid (fig.1), placea dot at the center of eachrosette.

Place the tracing paper overthe circle grid, and connectthe dots in horizontal anddiagonal lines to make atriangle grid.

fig. 1 Seven Overlapping Circles Grid

1. 2.

3.

For an example see Laila and Majnun at School:Miniature fromthe Khamseh of Nizami(slide 17)

In Activity 1, if you had continued adding overlapping circles at the intersection points,the result would be a circle grid as shown in the seven overlapping circles grid (fig. 1).This circle grid is the basis for both the triangle grid and the hexagon grid.


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From One Circle to Five Overlapping Circles

Activity 4

Bisect the page by drawingone horizontalandoneperpendicular line. Mark thecenter as A.

Place the compass point atpoint A and draw a circle.Leave room to draw equalsized circles on each side,at the bottom, and at the top.Mark the points that cross thelines B, C, D, and E.

Using points B, C, D, and E,draw four more circles.Mark the points where thefour circles intersect F, G, H,andJ.

Use a straightedge to drawthelines FH andJG throughthe center. These linesintersect the original circle atfour equally spaced pointsat K, L, M, and P.

The straight lines both dividethe circle into eight equalparts and locate eightequally spaced pointsB,C, D, E, K, L, M, Pon thecircumference of the originalcircle. This is the result of thefive circles having the sameradius. These points can beused to form octagons,eight-pointed stars, and four-

pointed stars, as shown inActivity 5.

paper,straightedge,compass,marker

AB B

C

D

E

F

GH

J

F

GH

J K

M L

P


Activity 5straightedge, markerfour copies of the fivoverlapping circles dmade in Activity 4

Octagon

To create a regular octagon, usea straightedge to join adjacentpoints on the circumference ofthe original circle.

Eight-pointed star,version 1By joining every secondpoint on the original circle,

you will create two squaresthat overlap to form aneight-pointed star.

Eight-pointed star,version 2By joining every third point,

you will create a differenteight-pointed star.

Four-pointed star

Embedded in the eight-pointed star (version 2)is a four-pointed star.

1. 2. 3.

4. 5.

For examples see Textile fragment (slide 13) andLeaf from a Quran manuscript (slide 16)


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For an example see Marquetry panel (slide 2)

In Activity 4, if you had continued adding overlapping circles at the intersection points,the result would be a circle grid as shown in the five overlapping circles grid (fig. 2).This circle grid is the basis for the square grid and the diagonal grid.

Now you have the squaregrid on the tracing paper.Using the straightedge anda different colored marker,mark diagonal lines.

Activity 6

Creating Square Grids from Circles

With the tracing paper overthe circle grid, connect thedots horizontally and verticallyto make a square grid.

On the five overlappingcircles grid (fig. 2), placea dot at the point whereeach circle meets.

fig. 2 Five Overlapping Circles Grid

1. 2.

3.

tracing paper, two differentcolored markers, straight-edge, five overlappingcircles grid (fig. 2)


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fig.7AActivity 7

Discovering Patterns within the Triangle Grid tracing paper, marker,triangle grid (fig. 3)

Place thetracing paper overtriangle grid (fig. 3).

Select any one of the threepatterns below and, on thetracing paper, copy onlythose lines that will create

your selected pattern. Usethe lines of the grid as aguide.

Repeat with the otherpatterns.

fig. 3 Triangle Grid

1. 2. 3.

For examples see Molded tile panel (slide 5) and Glazed tile panel (slide 6)


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Activity 8

Discovering Patterns within the FiveOverlapping Circles Grid

tracing paper, marker,five overlappingcircles grid (fig. 4)

Place the tracing paper overthe five overlapping circlesgrid (fig. 4).

Select any one of the threepatterns below and, onthe tracing paper, traceonly those lines that willcreate your selected pattern.Use the lines of the gridas a guide.


fig. 4 Five Overlapping Circles Grid

1. 2. 3.

For an example see Mihrab (slide 19)


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Activity 9

Discovering Patterns within the SevenOverlapping Circles Grid

tracing paper, marker,seven overlappingcircles grid (fig. 5)

Placethe tracing paper overthe seven overlappingcircles grid (fig. 5).

1. Select any one of the threepatterns below and, on thetracing paper, copy onlythose lines that will create

your selected pattern. Usethe lines of the grid as aguide.

2. Repeat with the otherpatterns.

3.

fig. 5 Seven Overlapping Circles Grid

For an example see Bowl (slide 1)


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Activity 10

Discovering Patterns within the Diagonal Gridtracing paper, marker,diagonal grid (fig. 6)

Place the tracing paper overthe diagonal grid (fig. 6).

Select one of the threepatterns below and, onthe tracing paper, traceonly those lines that willcreate your selected pattern.Use the lines of the grid asa guide.


fig. 6 Diagonal Grid

1. 2. 3.

For an example see Tile panel in the star-cross pattern (slide 7)


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Activity 11

Class Project with Cut-Out StarsConstructing and Decorating the Stars

compass, scissors, colored markers,circle (fig. 7), flat surface for mounting thefinished stars. (The flat surface can be a posterboard or paper. Size will depend on the number ofstars you have.)

Using fig. 7, begin bycarefully cutting out thecircle.

Measure line CD. At thehalfway point, mark pointE. Keeping a sharp pointat B, fold along line BE.Where C now touches thecircles edge, mark point F.

Hold the folded circle so you cansee where fold BE (created instep 4) meets the outer edge ofthe circle. Cut along fold line BE.

Fold B up to meet point F. Ifyou look at the folded circleedge on, it should make azigzag.

Unfold. Fold to the backalong axis CF.

Fold the circle in half. Fold A over to B.

Constructing a Six-Pointed Star

7

A B

A B

C

CC BCB

B

F

B

8. Open to discover six-pointed star.

Using fig. 7, begin bycarefully cutting outthe circle.

Fold B up to D, creating newpoint E.

Cut along fold lines EF andDG only to the intersection.

Draw a perpendicular from line CE to point DFold E down along linekeeping a sharp point Unfold.

Draw a perpendicular linefrom line CD to point E.Fold D down along line EF,keeping a sharp point at E.Unfold.

Fold the circle in half. Fold A over to B.

Constructing an Eight-Pointed Star

7

A B

A B

B

8. Open to discover an eight-pointed star.

D

B

D

E

D

E

D

E

D

D

D D

E E

F

FF

B

B

E

F

C

C

B

E

C

C

E

C C

CC

C

E

D

F F

F

D

EF

G

G

D

F E

G

1. 2. 3.

4. 5. 6.

7.

1. 2. 3.

4. 5. 6.

7.


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Ask the students to decorate their stars. Look at the slides for ideas for patterns and designs. We suggestthat the stars be placed on either a light colored or black background to enhance the students decoration.Each student can make multiple stars to form his or her own panel, or individual students stars can becombined to make a class panel. The stars should be mounted on the panel (poster board or paper) withtheir points touching, as shown below.

Decorating the Stars

Once the project is completed, you may want to point out the star-hexagon pattern in the Moldedtile panel (slide 5) and/or the Tile panel in the star-cross pattern (slide 7). Ask the studentsto compare these artworks to their own projects.

Once the project is completed, you may want to point out the star-hexagon pattern in the Moldedtile panel (slide 5) and/or the Tile panel in the star-cross pattern (slide 7). Ask the studentsto compare these artworks to their own projects.

Six-pointed star panel Eight-pointed star panel

fig. 7 Circle


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Resources and Glossary


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Selected Bibliography and Resources

slamic World

Al-Quran (The Quran). Trans. Ahmed Ali.Princeton, N.J.: Princeton University Press, 1984.

Armstrong, Karen. Islam: A Short History.Modern Library Chronicle Series. New York:Modern Library, 2000.

Armstrong, Karen. Muhammad: A Biography ofhe Prophet. New York: Harper Collins, 1992.

Shabbas, Audrey, ed. Arab World StudiesNotebook. Berkeley: AWAIR (Arab World andslamic Resources), 1998.

Turner, Howard R. Science in Medieval Islam:

An Illustrated Introduction. Austin: University ofTexas Press, 1997.he intellectual legacy left by the multinational and

multiethnic scientific community (Christians, Jews,and Muslims from all over the Islamic world) of theinth through thirteenth century is the subject of thislustrated, readable survey.

slamic Art

Baer, Eva. Islamic Ornament. Edinburgh:Edinburgh University Press, 1998.Baer presents an historic sur vey of the functionand significance of Islamic ornament spanningone thousand years, from the seventh througheventeenth century.

Blair, Sheila S., and Jonathan M. Bloom.The Art and Architecture of Islam, 12501800.New Haven: Yale University Press, 1994.Blair and Bloom, renowned scholars of Islamic art,provide a thoroughly readable and copiously illustrateddetailed look at Islamic art from the time of the Mongolnvasions in the thirteenth century to the beginning of theineteenth century; a final chapter covers Islamic ar t

and its relationship to the West in the nineteenth andwentieth centuries.

Bloom, Jonathan M., and Sheila S. Blair.slamic Arts. London: Phaidon Press, 1997.Beginning with a definition of Islamic art, Bloom andBlair then describe it in this excellent, readableone-volume introduction.

Carboni, Stefano, and David Whitehouse.Glass of the Sultans. New York: The MetropolitanMuseum of Art; Corning: Corning Museum ofGlass; Athens: Benaki Museum; New Haven:Yale University Press, 2001.Featuring more than 150 glass objects representing twelve centuries of Islamic glassmaking, thisbeautifullyillustrated exhibition catalog includes essays on thehistory as well as the techniques of glass making.

Ettinghausen, Richard, Oleg Grabar, andMarilyn Jenkins-Madina. Islamic Art andArchitecture, 6501250. New Haven:Yale University Press, 2001.This is an overview of Islamic ar t and architectureof Spain, Africa, and the Middle East from itsbeginnings to the mid-thirteenth century. Written by

well-known scholars, this amply illustrated and readablebook provides a well-balanced account and makesthe age and its art come alive for the student and thegeneral reader.

Robinson, Francis, ed. Cambridge IllustratedHistory of the Islamic World. Cambridge:Cambridge University Press, 1996.An outstanding one-volume overview of the entire Islamicworld from its rise in the s eventh century to the end of thetwentieth; well illustrated and engaging, it includes achronology of all rulers and an extensive bibliography.

Stierlin, Henri. Islamic Art and Architecture.London: Thames and Hudson, 2002.Stierlin, an architectural historian, has written a lavishlyillustrated overview of Islamic art and architecture; thebook includes detailed presentations on nine of the gre atmasterpieces of Islamic architecture, including the FridayMosque in Isfahan and the Taj Mahal in Agra.

Math and Geometry

Bourgoin, Jules. Arabic Geometrical Pattern andDesign. New York: Dover Publications, 1974.This book of patterns illustrates 190 examples of Islamic

geometrical designs: hexagons, octagons, pentagons,heptagons, dodecagons, and more.

Critchlow, Keith. Islamic Patterns: An Analyticaland Cosmological Approach. New York: Thamesand Hudson, 1984.Through progressively complex geometricalprocedures, the author provides a foundation frombasic building blocks of Islamic geometrical patternsto multifaceted designs.

El-Said, Issam. Islamic Art and Architecture:The System of Geometric Design. Reading, U.K.:Garnet Publishing, 1993.This is a consideration of the background and construction of Islamic design. Written for the authorsdoctoral thesis, it explains the mathematical elementsbehind the designs.

Forseth, Sonia Daleki. Creative Math/Art Activitiesfor the Primary Grades. Englewood Cliffs, N.J.:Prentice-Hall, 1984.These lessons are designed to supplement and reinforcebasic concepts for mathematics instruction fromkindergarten through grade 3.

Henry, Boyd. Experiments with Patterns inMathematics: Enrichment Activities for Grades

712. Palo Alto, Calif.: Dale SeymourPublications, 1987.These fifty -five experiments utilizing patterns andnumbers provide a wealth of ideas from polygonalnumbers through pythagorean triples.

Newman, Rochelle, and Martha Boles. The GoldenRelationship: Art, Math, Nature. Book 1. UniversalPatterns, 2nd rev. ed. Book 2. The Surface Plane.Bradford, Mass.: Pythagorean Press, 1992.Art and mathematics constructs are used here to helpmake connections and understand the recurring patternsin nature and in space. Forms and words are linkedto explore patterns. Appendices include mathematicalsymbols, properties, and proofs; geometric formulas;art techniques; templates; and an illustrated glossary.

Norman, Jane, et al. Patterns East and West:Introduction to Pattern in Art for Teachers. NewYork: The Metropolitan Museum of Art, 1986.Examples from a cross-section of the MetropolitanMuseums collection are compared, analyzed, andtransformed (includes slides).Stevens, Peter. Handbook of Regular Patterns:An Introduction to Symmetry in Two Dimensions.Cambridge, Mass.: MIT Press, 1981.

Stevens combines artistic symbols with mathematicalexplanations and relates designs from different culturesand periods in history.

Wade, David. Pattern in Islamic Art. Woodstock,N.Y.: The Overlook Press, 1976.This pattern book illustrates the structure anddevelopment of Islamic patterns and providesdescriptions and directions for construction.

Juvenile

Beshore, George. Science in Early Islamic Culture.Science of the Past. New York: Franklin Watts, 1998.Concise chapters on science, numbers, astronomy,geography, and medicine highlight these achievementsin the Islamic world and their continuing impact onWestern civilization.

George, Linda S. The Golden Age of Islam.Cultures of the Past. New York: Benchmark Books,1998.Covers the history, beliefs, society, and global legacyof Islam from the last years of the eighth century to thethirteenth century.

MacDonald, Fiona. A 16th-Century Mosque. Inside

Story. New York: Peter Bedrick Books, 1994.The design and construction of Istanbuls Suleymaniyemosque by the famous architect Sinan is the context for adiscussion of all aspects of life in the Ottoman empire ofthe sixteenth century.

Videos

Islam. Produced and directed by Steve York; writtenby Michael Olmert. Alexandria, Va.: PBS Video,1991. (VHS 58 min.) Smithsonian World(television program)Examines the history and culture of Islam.

Islam: A Civilization and Its Art. Produced anddirected by Jo Franklin. Washington, D.C.:Pacific Productions, 1991. (VHS 90 min.)An informative and entertaining look at Islamic artand culture.

Other Sources

Timeline of Art Historywww.metmuseum.org/toah

The Math Forumhttp://mathforum.orgThe Math Forum is a research and educational enterpriseof Drexel University; the site has information and links forK12, college, and advanced math topics.

Aramco World MagazinePublished six times annually to increase cross-culturalunderstanding of Arab and Muslim worlds. Freesubscription for educators: Saudi Aramco World, Box469008, Escondido, CA 92406-9008


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Glossary

Allahhe Arabic word for God, the samemonotheistic God worshipped in Judaismand Christianity, the God of Abraham,he God of Jesus

calligraphyhe art of elegant or stylized writing inwhich the word itself becomes a workof art: exceptionally skilled Muslimalligraphers gained honorific titles

and fame

cartouchea decorative oval or oblong-shapedpanel with scrolled edges used in artand architecture as a base fornscriptions or other decorations, orsed as a decoration in and of itself

cenotapha tomblike monument or memorialdedicated to a deceased person whos buried elsewhere

circlea plane figure bounded by a singleurved line, every point of which is

equally distant from the point at theenter of the figure

equilateral trianglea triangle whose three sides are ofequal length

Hadithslams second holiest book, literallytraditions or accounts of

Muhammads actions, sayings, andommentaries on the Quran, whichogether form the basis of Islamic law

dolatryhe worship of idols, or images of deities

slamterally surrender, submissiono the will of God; the religionpromulgated by Muhammad andollowed today by about one-quarterof the worlds population

Kuficscriptcoming into use in the seventh century,this was used primarily for monumentalpurposes, its angular forms ideal forarchitectural decoration

marquetrydecoration achieved by inlaying patternsinto precious woods or ivory

mihraba recessed niche in a mosque wallthat indicates the direction of Meccaand marks the focus of congregationalprayers, usually the most adorned anddecorated element of the mosque

minaiwarea Persian style of pottery in which mostcolors are applied over the glaze

mosque (masjid)literally place of prostration, whereMuslims gather for prayer; a newmosque is built where the calls toprayer from the nearest mosque canno longer be heard

Muhammad(b. Mecca, Arabia, ca. 570 A.D.,d. Medina, 632 A.D.) recognized asthe messenger of God by the Muslims,he was an Arab merchant who preachedthe Islamic faith, began receiving divinerevelations about 610 A.D., and wasforced to leave with his followers fromMecca to Medina in 622 A.D.

muqarnasinitially structural in purpose and madeof stone, later decorative and crafted ofplaster, these clustered niches or partsof niches were used to decorate the areabetween the walls and dome in Islamicarchitecture (also known as honeycombor stalactite vaulting)

Muslima follower of Islam, literally one whosurrenders, hence, one who has directaccess to his/her God (Islam havingno priesthood)

omphalosfrom the Greek word for navel, adecorative motif consisting of a bumpor knob within a circle

polygona plane figure with several angles andsides, usually more than four (see alsoregular polygon)

Quranliterally recitation, the holy book ofIslam, containing Gods words asrevealed in Arabic to Muhammad; theQuran contains 114 suras, or chapters

regular polygona polygon with equal sides and equalangles, e.g., an equilateral triangle,square, pentagon, hexagon, heptagon,or octagon (see also polygon)

regular tessellationthe only three regular tessellationsthat can exist are the tessellations byequilateral triangles, by squares, andby hexagons; the boundaries of thesetessellations form the triangle grid, thesquare grid, and the hexagon grid(see also tessellation)

symmetrycorrespondence in size, shape, andrelative position of parts on oppositesides of a dividing line or medium planeor about a center or axis

tessellationa covering of an infinite geometric planewithout gaps or overlaps by congruentplane figures of one type or a few types(see also regular tessellation)

vegetal motifsdecoration reminiscent of plants, usuallycharacterized by curving,twisting linear

forms such as stalks or stems, as well asfloral or leaf patterns


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İslamic art and geometry design

Documents