41. History Of Architecture Director of the pyramids. . Sphinx photographs . Valley of the Kings, tomb ofTutankhamun. Empire State Building, New York. . F. Florentine architecture. http://www.zeroland.co.nz/architecture_history.html

Film Music Literature Philosophy ... Store The History of Architecture Architects by name Architecture and Architects by Country General architecture resources The History of Architecture A - E F - J K - P Q - Z A Alberti, Leon Battista American architecture. The Digital Archive of American Architecture. Architects. Famous architects. Great architects online.Biographies, image galleries. Venturi, Philip Johnson, Isozaki, Ando, Gropius and others. Athens. The Ancient City of Athens. Maps, photographs, essays. ... Art Deco Society. International internet Art Deco resources. Baroque architecture Baroque and Renaissance architecture. An image database from The University of Virginia. Brunelleschi, Filippo. Brunelleschi images Castles Castle Eltz, Germany Castles on the Web. A Photo Archive of castles, categorized by country. Castles of the World. A comprehensive directory of castles in Europe and around the world. Castles include Neuschwanstein, Versailles, Amboise, Chambord, Linderhof, Bouillon, Angers, Chenonceau, Chilllon, Mount St. Michael. Chateaux de France. French Chateaux. Chateau site ... Chicago Museum of Architecture and Design. The Atheneum. Buildings of Chicago. Churches, cathedrals Baroque churches in Salzburg Byzantine Church Architecture Catholic Church Architecture Church architecture around the world. Ecclesiological Society. Links, furnishings, liturgy.

42. Egyptian Architecture Egypt game. Temples , pyramids , palaces, statues, and altars are examplesof the great Egyptian architecture. architecture is very http://bulldog2.berwick-academy.so-berwick.pvt.k12.me.us/projects/Egypt_Game/arc

Architecture Architecture plays a main role in the Egypt Game. The characters often use the things in the shack to make temples and altars to the ancient Egyptian gods. They also used their imagination to make an oracle out of the old artifacts. www.ancientegypt.co.uk/menu.html click on Temples Questions 1) How did the hypostyle hall of the Temple represent a marsh? 2) Who could enter the sanctuary of a Temple? 3) What was the sacred lake and what was it used for? www.ancientegypt.co.uk/menu.html click on Pyramids Questions: 1) Why were pyramids built 2) Where were the largest pyramids? 3) What are casing blocks and why aren't they part of the pyramids today? find your way inside the Pyramid to explore: 4) What are 2 possible reasons the pyramids have air shafts? 5) Find the King's chamber. Why is it almost empty today? 6) Why is "Queen's Chamber" a misleading name? www.eyelid.co.uk/pyr-temp.htm 1. What does the Udjat eye represent? Click on: Giza 2.What time of year did the farmers build the pyramid at Giza and why? Click on: Temple of Dendara 3.What goddess is the temple of Dendara named for, and what is she the goddess of?

43. Great Pyramid Of Khufu - El Giza, Egypt - Great Buildings Online The pyramids at Giza—descendants of primitive stepped prototypes built insuperimposed layers—are gigantic prisms unique in world architecture, http://www.greatbuildings.com/buildings/Great_Pyramid.html

Great Pyramid of Khufu Great Buildings Online Search Advanced Search Buildings ... ArchitectureWeek Architect unknown Location El Giza, Egypt Date -2600 to -2480 Building Type pyramid tomb, monument Construction System bearing masonry (cut stone) Climate desert Context rural Style Ancient Egyptian Notes "Pyramid of Cheops" or "Khufu's Pyramid", near Cairo, the farthest north and east of the famous trio, often the pyramid in back in the classic picture. Ancient Egyptian, Fourth Dynasty Images Photo, overview of the pyramids Photo, Khafre's Pyramid Photo, overview of the Sphinx Photo, interior detail ... Photo, overview at dawn More Images Poster Image - Pyramids of Giza Poster Image - Pyramids in the Distance, Across the Water Poster Image - Pyramids, Moon, and Sand Dunes Drawings Site Plan Drawing ...more drawings available on The GBC CD-ROM 3D Model Model Viewing Instructions Discussion Great Pyramid of Khufu Commentary Details Khufu or Cheop's Great Pyramid is 756 feet (241 meters) square in plan, and 481 feet (153 meters) high. The angle of inclination of the triangular faces is about 51.5 degrees. The square of its height equals the area of each triangular face, as determined by Herodotus in 450 B. C. The base of the pyramid covers about 13 acres. The other two pyramids in the famous trio are Khafre, 704 feet (214.5 meters) square, 471 feet (143.5 meters) high, with a face inclination of 53.2 degrees, and Menkaure, 345.5 feet (110 meters) square, 216 feet (68.8 meters) high, with a face inclination of 51.3 degrees (or possibly 330ft wide and 206 ft high (105m x 65.5m)).

44. Thais - Egiptian Architecture - Index Of Locality Frontal view with the pyramids, IV Dynasty ( 25702135 BC). The Cheops Pyramid, LowerTemple, passage to the pillared T-shaped chamber, IV Dynasty ( 2570- 2135 BC). http://www.thais.it/architettura/egizia/indici/indxloc_uk.htm

LOCALITY' SUBJECT DESCRIPTION ERA Abu Simbel Rocky Temple of Ramses II Details of the facade XIX Dynasty ( 1305-1196 B.C.) Details of the facade XIX Dynasty ( 1305-1196 B.C.) ... Email

45. Thais - Egiptian Architecture - The Sphynx And The Pyramids Of Cheops And Chephr SUBJECT The Sphynx and the pyramids of Cheops and Chephren. DESCRIPTION TheCheops Pyramid on the right and that of Chephren on the left. LOCALITY Giza. http://www.thais.it/architettura/egizia/schede/sc_00019_uk.htm

PERIOD: Thinite era and Old Kingdom ERA: IV Dynasty ( 2570- 2135 B.C.) SUBJECT: The Sphynx and the pyramids of Cheops and Chephren DESCRIPTION: The Cheops Pyramid on the right and that of Chephren on the left LOCALITY: Giza LOCATION: NATION: Egypt AUTHOR: Email

46. Egyptian Architecture Egyptian architecture. The ancient Egyptians used the golden ratio in much oftheir artwork, including in heiroglyphs, the pyramids, and many statues. http://www.geocities.com/CapeCanaveral/Station/8228/earch.htm

Egyptian Architecture The ancient Egyptians used the golden ratio in much of their artwork, including in heiroglyphs, the pyramids, and many statues. The Ahmes papyrus of Egypt gives an account of the building of the Great Pyramid of Giza in 4700 B.C. with proportions according to a "sacred ratio." Modern measurements show that the ratio of the distance from groud center to base edge, to slant edge of the pyramid is amost exactly 0.618. The sides of the pyramid appear to be golden triangles. A golden triangle is an isosceles triangle with base angles of 72º and a vertex angle of 36º. The picture above shows that the apothem (central height) of any of the side triangles of the pyramid relate to half the base in the proportional ratio of the golden section. In cubits (the measurement used by ancient Egyptians): 1/2 base = 220; apothem = 356; 356:220 = 1.618 Also, the 3-4-5 triangle is the golden ratio between its 5 unit side and 3 unit base. The Egyptians thought this was of vital importance. They used this triangle in many ways, such as a surveying tool and in the pyramids. The three oldest Giza pyramids lay on a Fibonacci spiral and the opening to the Hall of Records is geometrically marked by the lines which bisect the golden rectangle.

47. ArtLex On Architecture The pyramids at Giza are descendants of earlier stepped designs which were builtin superimposed layers. They are gigantic prisms unique in world architecture. http://www.artlex.com/ArtLex/a/architecture.html

a rchitecture - The art of designing and constructing buildings ( structures ), and other environmental features. A person who practises architecture is called an architect The jargon of architecture is what architects and designers archly call "talkitecture" or "archispeak." They refer to windows as " glazing " or " fenestration ," and a beam or lintel as " trabeation ." A covered driveway is a "porte-cochere." Nothing is simply flat , it's " planar " instead. Construction people are content with solid Anglo-Saxon words: wall, window, and door. Architects add a savory salad of Latin- and French-based words. Architects eschew gustatory metaphors like my salad, but they can't hold back from using the human body as metaphor: a building can have arms, head, spine, skeleton, skin, etc. Western periods of architectural history generally parallel those of the other arts: classical Gothic Renaissance Mannerism ... Modernism , and Postmodernism among them. Some examples of architecture: England, Salisbury Plain

48. Mathematics And Architecture Historically, architecture was part of mathematics, and in many periods mathematicianswere architects, whose constructions the pyramids, ziggurats, temples http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Architecture.html

Mathematics and Architecture Alphabetical list of History Topics History Topics Index Although many readers of this archive might find an article on mathematics and architecture a little surprising, in fact architecture was in ancient times considered a mathematical topic and the disciplines have, up to the present time, retained close connections. Perhaps once one realises that mathematics is essentially the study of patterns, the connection with architecture becomes clearer. Salingaros writes in [27]:- Historically, architecture was part of mathematics, and in many periods of the past, the two disciplines were indistinguishable. In the ancient world, mathematicians were architects, whose constructions - the pyramids, ziggurats, temples, stadia, and irrigation projects - we marvel at today. In Classical Greece and ancient Rome, architects were required to also be mathematicians. When the Byzantine emperor Justinian wanted an architect to build the Hagia Sophia as a building that surpassed everything ever built before, he turned to two professors of mathematics geometers , Isidoros and Anthemius , to do the job. This tradition continued into the Islamic civilization. Islamic architects created a wealth of two-dimensional tiling patterns centuries before western mathematicians gave a complete classification.

49. The Maya: Places And Pyramids Of The Rainforest (Architecture And Design Series) The Maya Places and pyramids of the Rainforest (architecture andDesign Series). The Maya Places and pyramids of the Rainforest http://www.fortamherst.co.uk/The-Maya-Places-and-Pyramids-of-the-Rainforest-A-67

The Maya: Places and Pyramids of the Rainforest (Architecture and Design Series) Title: The Maya: Places and Pyramids of the Rainforest (Architecture and Design Series) Subject: Ancient General Category: Art Architecture Photography General Format: Paperback Bill Dobbins-Modern Amazons... Christian Wurster-Computers: An Illustrated History... Hartmann Schedel Stephan Fussel-The Nuremburg Chronicle of the World (Taschen Jumbo Series)... H R Giger-Giger (Art Albums)... ... Gibbon and Siamang: Evolution,Ecology,Behaviour and Captive Maintenance...

50. TASCHEN Books: Architecture - All Titles - The Maya - Palaces And Pyramids Of Th his presentation of these most remarkable examples of Mayan architecture on the inthe depths of the rain forest, along with soaring pyramids, mysterious tombs http://www.taschen.com/pages/en/catalogue/books/architecture/all/facts/00242.htm

A key to unlock the mystery of 1200 years of Mayan architecture Architecture - All Titles - The Maya - Palaces and pyramids of the rainforest - Facts The Maya - Palaces and pyramids of the rainforest Edited by: Stierlin, Henri Author(s): Stierlin, Henri Softcover, 240 x 300 mm, 240 pages The most remarkable examples of Mayan architecture The author and editor Henri Stierlin has based his presentation of these most remarkable examples of Mayan architecture on the latest findings from excavations in Mexico, Guatemala, Honduras and Belize. Cities have been rediscovered in the depths of the rain forest, along with soaring pyramids, mysterious tombs, palaces with frescoes and steles. Particularly intriguing is the fact that, although this very advanced civilisation evolved completely separately from that of the "Old World", the architectural parallels are astonishing. Only very recently has it been possible to decipher Mayan hieroglyphics to any great extent. This new research is used to full advantage by this volume as a key to unlock the mystery of Mayan architecture. Editions: Dutch: 3-8228-1243-9 English: 3-8228-1241-2 French: 3-8228-1242-0 German: 3-8228-1240-4 Spanish: 3-8228-1273-0 List Prices: Buy it now At your local bookstore or in association with Amazon: Reviews This is such a great book! The pictures and plans are detailed and the writing is well researched and in depth. For anybody wanting information on the Maya for work or,like me,are just interested in the maya then this is a must!

51. TASCHEN Books: Architecture - All Titles - The Maya - Palaces And Pyramids Of Th Softcover, 240 x 300 mm, 240 pages A compendium of 3000 years of architecturalhistory in Egypt, featuring the most impressive pyramids, tombs and temples. http://www.taschen.com/pages/en/catalogue/books/architecture/all/seealso/00242.h

A key to unlock the mystery of 1200 years of Mayan architecture Architecture - All Titles - The Maya - Palaces and pyramids of the rainforest - See also The Maya - Palaces and pyramids of the rainforest Edited by: Stierlin, Henri Author(s): Stierlin, Henri Softcover, 240 x 300 mm, 240 pages See also Egypt - From Prehistory to the Romans Hardcover, 240 x 300 mm, 240 pages Publishing Date: July 2004 A compendium of 3000 years of architectural history in Egypt (Spanish hardcover edition) Egypt - From Prehistory to the Romans Author: Wildung, Dietrich Softcover, 240 x 300 mm, 240 pages A compendium of 3000 years of architectural history in Egypt, featuring the most impressive pyramids, tombs and temples Greece - From Mycenae to the Parthenon Hardcover, 240 x 300 mm, 240 pages Publishing Date: July 2004 A comprehensive introduction to the architecture of Greek antiquity - the architecture of perfect harmony and proportion (Spanish hardcover edition) Greece - From Mycenae to the Parthenon Author: Stierlin, Henri Softcover, 240 x 300 mm, 240 pages

52. Insight Books - Pyramids & Other Egyptian Architecture/archeology pyramids Other Egyptian architecture/archeology at Insight Metaphysical Bookstore. Found38 items in pyramids Other Egyptian architecture/archeology. http://www.insight-books.com/PRMD

document.write(dtt); Home Subjects Sidelines About Us ... Shopping Cart title author in keyword subject ISBN Advanced Search Pyramid Handbook This book is a complete handbook about the pyramids of Ancient Egypt during the Pyramid Age It contains the locations and dimensions of the ... Read About It Moustafa Gadalla US $ 11.95 Thoth: Architect Of The Universe While researching the metrology of the megalithic monuments of Britain and Egypt the author made an astounding observation these monuments can ... Read About It Ralph Ellis US $ 16.00 Voyages Of The Pyramid Builders: The True Origins Of The Pyramids From Lost Egypt To... Did ancient peoples from Egypt and South America to the Celts and early Buddhists all spontaneously dream up the idea of building pyramids A ... Read About It Robert M. Schoch US $ 16.95 Ancient Egypt David P. (Ed.) Silverman US $ 19.95 Giorgio Agnese US $ 17.99 Ancient Egypt: Glorious Treasures Karen Sullivan US $ 10.98 Art And History Of Luxor NSA US $ 14.95 Building The Great Pyramid US $ 19.95 Complete Gods And Goddesses Of Ancient Egypt Richard H. Wilkinson

53. TeacherSource . Math . Architecture . Community Geometry | PBS pyramids? (pyramids come to a point, and their sides are triangles. town?Are there any cone shapes in the architecture in your town? http://www.pbs.org/teachersource/mathline/concepts/architecture/activity2.shtm

search options Friday, June 11, 2004 Community Geometry (Grade Levels: 3 - 7) Building Materials Community Geometry Bridge Builder Career Connections ... More Math Concepts The great thing about geometry is that it is all around us! And the architecture of buildings and objects provides a perfect setting for students to look at and find shapes and geometric properties. It is wonderful to help students to see the mathematics in the shapes and designs of the world around them. You might use some or all of these activities: Create a geometry slide show: Take slides of architectural structures and objects that represent different figures and types of geometry and mathematics. This can include slides from other places but should also include slides of buildings or objects that the students will easily recognize as being in their school and community. You can use these slides at the beginning of the geometry unit when you are learning about or reviewing names of different object and their properties. Slides work well for this activity because they allow everyone to see the same picture at the same time and to talk about the geometry in that picture.

54. NOVA Online/Pyramids/Interview With Mark Lehner but the architecture that they built out of the mud of the valley floor which isin fact where they lived. And so there s a whole counterpart to the pyramids, http://www.pbs.org/wgbh/nova/pyramid/excavation/lehner.html

Interview with Mark Lehner, Archaeologist, Oriental Institute of the University of Chicago, and Harvard Semitic Museum NOVA: Can you briefly tell us about your history at Giza and tell us about some of the work you've done there? In essence, why Giza? LEHNER: Wow, do you want the real answer or the abridged version? I first went to Egypt in 1972 as a tourist. And then I went back in 1973, the following year as a year abroad student at the American University in Cairo. And it's no secret that when I went I myself was imbued with the ideas of lost civilizations and inspired by a man named Edgar Cayce. So I was in fact, myself, looking for the lost civilization and something called the Hall of Records. Hear Lehner via RealAudio: dialup broadband Get RealAudio plugin Or at least those ideas were on my mind. To make a long story short, those ideas didn't stand up against bedrock reality. And so then I was still fascinated by these pyramids and the Sphinx. Then I asked the question, well, what is the real story? What is the story that the site itself has to tell. And so that's what sustained me and kept me out there in a kind of exploratory mode. NOVA: Why do we still have only limited knowledge about Giza and the construction of the pyramids there? And how do we know what we know about Giza?

55. Index Of Art Historical Sites. Digital Imaging Project: Art Historical Images Of by Julia Morgan) See also Index to Sculpture and architecture by African Satet GizaFunerary boat ( Solar boat ) of King Cheops (Khufu) pyramids and Environs http://www.bluffton.edu/~sullivanm/index/

MORE THAN 10,000 IMAGESAND MORE TO COME INDEX OF ART HISTORICAL SITES (SCROLL DOWN) Note: Images from Vietnam and Cambodia and NEW Images from Mexico (especially Mayan and Olmec sites) Zaha Hadid, Winner of the Pritzker Architecture Prize for 2004, considered the profession's highest honor. She is the first woman to receive it. Contemporary Arts Center, Cincinnati, 2003 (24 imagesmore interiors will be posted later) Featured site for April, 2004 Uxmal Archaeological Site, Mexico (72 images) Featured site for March, 2004 East Building, National Gallery of Art by I. M. Pei (36 images) Featured site for February, 2004 Mayan Archaeological Site (33 images) Featured site for January, 2004 Genesis, the Gift of Life , Dallas Museum of Art, glass mosaic, 1954, by Miguel Covarrubias (10 images) See earlier featured sites here. Click here to go to the index of artists and architects. Click here to go to the chronological index. NOTE Web Creator's comments: philosophy, technical issues, use of images, etc. Links Go Key Resource ... #4 in Picture Collections Topic INDEX OF ART HISTORICAL SITES Austria Canada Egypt France ... United States See also Women Architects (with more than 60 buildings by Julia Morgan) See also Index to Sculpture and Architecture by African American Artists or Relevant to African American History and Culture Austria Vienna Apartment Block No. 38 (Wagner)

56. MSN Encarta - Egyptian Art And Architecture II. Predynastic Egypt (50003000 bc). III. Dynastic Egypt (3000-30 bc). A. architecture.1. Royal Tombs and pyramids. 2. Tombs of the Elite. 3. Temples. 4. Palaces. http://encarta.msn.com/encyclopedia_761560148/Egyptian_Art_and_Architecture.html

MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Subscription Article MSN Encarta Premium: Get this article, plus 60,000 other articles, an interactive atlas, dictionaries, thesaurus, articles from 100 leading magazines, homework tools, daily math help and more for $4.95/month or $29.95/year (plus applicable taxes.) Learn more. This article is exclusively available for MSN Encarta Premium Subscribers. Already a subscriber? Sign in above. Egyptian Art and Architecture I. Introduction Egyptian Art and Architecture , the buildings, sculpture, painting, and decorative arts of ancient Egypt from about 5000 bc to the conquest of Egypt by... II. Predynastic Egypt (5000-3000 bc III. Dynastic Egypt (3000-30 bc A. Architecture Royal Tombs and Pyramids Tombs of the Elite Temples Palaces B. Sculpture The Purpose of Sculptures Sculptural Style and Materials C. Painting and Relief D. Decorative Arts E. The Amarna Period (1353 bc bc IV.

57. MSN Encarta - Search Results - Pyramids (Egypt) 8. Giza pyramids Egyptian architecture*. 15. Pyramid (architecture) picturesof pyramids Egyptian Archaeological Dig. Picture—Encarta Encyclopedia. http://encarta.msn.com/Pyramids_(Egypt).html

MSN Home My MSN Hotmail Shopping ... Money Web Search: logoImg('http://sc.msn.com'); Encarta Subscriber Sign In Help Home ... Upgrade to Encarta Premium Search Encarta Encarta Search results for "Pyramids (Egypt)" Page of 2 next Exclusively for MSN Encarta Premium Subscribers Pyramids (Egypt) Article—Encarta Encyclopedia Pyramids (Egypt) , large structures with four triangular sides that meet in a point at the top, directly over the center of the pyramid’s square base.... article outline Introduction What Is a Pyramid? The Great Pyramid How the Pyramid Form Developed ... Studying the Pyramids related items Ancient Egypt Egyptian Art and Architecture Seven Wonders of the World see also ... Ancient Egypt Article—Encarta Encyclopedia Ancient Egypt , civilization that thrived along the Nile River in northeastern Africa for more than 3,000 years, from about 3300 bc to 30 bc . It was... Old Kingdom Pyramids Sidebar—Encarta Encyclopedia This National Geographic article examines some of the new theories archaeologists have developed about Egyptian civilization during the period of... Egyptian Pyramids Picture—Encarta Encyclopedia Picture from Encarta Encyclopedia Land of the Weird: 8 Kooky Roadside Attractions Encarta Feature MSN Encarta columnist Martha Brockenbrough explores the kitschy side of roadside America.

58. Egyptian Architecture questia.com. History for Kids! Egyptian architecture (pyramids) Read about thetombs the ancient Egyptians built for their pharaohs. www.historyforkids.org. http://www.spectster.com/cgi-bin/search/smartsearch.cgi?keywords=egyptian archit

59. Prayer, Telepathy And Astrology: Connexions With Ancient Architecture, Pyramids, Similarly, the one thing common to pyramids is mass which leads to the nor the Gothicistswere wrong in their differing advocations for church architecture? http://www.mistral.co.uk/hammerwood/earthwav.htm

Buildings and landscapes, temples, Mother of all - Earth, the physics of invisible and immortal David Pinnegar BSC ARCS An old man once asked what was the difference between someone from the town and someone from the countryside. " The town man ", he said, " is clever. The country man is wise Town men might laugh at the bee-keeper talking to his bees or the seedsman talking to his plants and tell them that they are mad. When a swarm of wild bees in the walls of Hammerwood heard a bee-keeper proposing to kill them for fear of the spread of disease, the bees heard him and felt my fear for them! Within two hours they had fled elsewhere. Increasingly that which was unimaginable is now understandable. What would the medieval peasant have thought about that biblical story of Adam being put to sleep, cut open, the extraction of a rib and his being sewn back together, alive? In the past, life was simple - it was all a matter of belief. As we ate of the tree of knowledge, life became less clear. With imperfect knowledge Darwinists told us that we evolved from a primeval sea of life and they disrupted the faith of many. Yet scientific understanding of the DNA mechanism may yet confirm conclusively our old beliefs. If life ever evolved from chaos, the ancient myths suggest that it did so in another creation. What was light long ago has faded into darkness. Imperfect knowledge plunges us into a sea of uncertainty but in the deeper knowledge of science we rediscover the beauty of creation. The job common to artists, priests and scientists is to make that which was invisible visible. The task of the museum curator is to preserve the source materials.

60. Mathematics In Art And Architecture Fibonacci numbers. Growth and ratios in nature. Proportions in the human body.Proportions in architecture. The proportions of the Egyptian pyramids. http://www.math.nus.edu.sg/aslaksen/teaching/math-art-arch.shtml

Mathematics in Art and Architecture (GEK1518) Melencolia I by Albrecht D¼rer, 1514 The Ambassadors (1533), by Hans Holbein the Younger (1497/8 - 1543) Welcome to Mathematics in Art and Architecture! Objectives of the Module Topics to be Covered Practical Information and Assessment IVLE Course Page with Discussion Forum ... Recommended Texts Course Content Pyramids The Golden Ratio The Platonic Solids and Polyhedra Perspective ... Music Additional Information Lecture Notes Tutorials and Homework Assignments Old Exams Past Homework ... Luca Pacioli by Jacopo de Barbari, 1495 Objectives of the Module The goal of the course is to study connections between mathematics and art and architecture. You will see how mathematics is not just about formulas and logic, but about patterns, symmetry, structure, shape and beauty. We will study topics like tilings, polyhedra and perspective. After taking this course you will look at the world with new eyes and notice mathematical structures around you. Raphael's School of Athens, 1510-11 Topics to be Covered We start by studying tilings . They occur in many settings, and have a rich mathematical structure.

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