What type of architecture?

Asian Architecture

What type of architecture?

American Architecture

What type of architecture?

European Architecture

What type of architecture?

Islamic Architecture

What type of architecture?

Egyptian Architecture

How could you tell?  Many nations have similarities in their architecture,

but each puts their own uniqueness to it.

Can Architecture Define a nation?  “Until the invention of the printing press, architecture

was the primary means of the expression and communication of the ideas, values, and beliefs of a culture.” (Hendrix, 2010).  “One can tell more about a civilisation from its

architecture than from anything else it leaves behind.” (Clark, 1969).

Key Similarity  Majority of nations take

architectural ideas from other countries/regions to use; but they always change something to make it their own.  All nations need to use

mathematics to create their buildings!

Egyptian Architecture  Use many unique architectural elements  Built sturdy mud-brick pyramids  Pylon – Monumental entryway  Column - 2 different types  

Temple of Luxor

Open papyrus – flared at the top Closed papyrus – bulged at the top

 Obelisk - Tall, thin, four-sided spike of stone with

inscription on the side to praise the pharaoh who commissioned it

Mathematics in Ancient Egypt  Had very basic math skills, but unknowingly relied

heavily on Geometry.  Used own measures (cubits), math, tools (ropes) and nature sunlight (solar worship/science) to figure out how to build sound structures.  Architects of their time: Harpedonaptai (rope stretcher)  Created straight lines

 Right angle unknowingly used Pythagorean triplet when

building pyramids

Relations to Egyptian architecture?  Columns  Greeks, Romans and Europeans also use columns  Egyptians structured their columns differently  Obelisk  America has the Washington Monument 

Much larger in size

 Egyptian obelisks have hieroglyphics written all along

the obelisk in honor of the pharaoh it was built for

Greek Architecture  Columns are unique  Followed strict building order

 3 styles  Doric – most basic  Ionic – thinner and more elegant than Doric  Corinthian – very elaborate. Did not use as much of

Mathematics in Greece  Greek philosophers were considered first true

mathematicians  Pythagoras: 580-500BC  Greek philosopher who sought to interpret the entire

physical world in terms of numbers.  Best known for theorem on the right triangle  With music, discovered significance of dividing musical scale into ratios to create harmony. This lead to architects designing buildings with ratios and the use of a module, basic unit of length of a building

 Symmetry – Comes from Greek word “symmetria”

which means repetition of shapes and ratios

Relation to Greek Architecture Greek

Roman

 Temples were built on

 Temples were built on an

platform called a stylobata  Temples are built with vague entrance  Statues are placed in the cella, the room of the temple which no one was allowed to enter

elevated plateau  Temples had very definite entrances  Roman statues were placed in the center of the temple.  Had own Column, Composite Column, mixture of Ionic and Corinthian

Islamic Architecture  Islamic Doctoral Cannon  Calligraphy 

Al-Quran

Most sacred form of writing, used to write Quran

 Geometric 

Since it’s more vague than calligraphy, architect has opportunity to show skills

 Arabesque 

Seen across a wide range of mediums, from books to carpets and textiles

Temple ceiling

Mathematics in Islam  Islamic Decorative canon has remarkable similarity to

quasi-crystal patterns  Quasi-crystals – Are made when man takes natural elements

from periodic table to create man-made solids  Peter J Lu from Harvard examined mosaics from Middle East to determine their patterns, which are far more advance than anyone ever thought. To create quasi-crystallized design, used girih tiles, set of 5 shapes:     

Decagon Hexagon Bow tie Rhombus Pentagon Islamic tile pattern

Atomic model of quasi-crystal aluminum-palladiummanganese

Relations to Islamic Architecture?  Europe  Cathedrals  

Rose stained class geometric patterns Geometric pattern used for religious window decoration. Middle East does not use it for the same purpose

 Calligraphy 



Europeans copied calligraphy style in Renaissance The middle east only use it for religious writing though

European Architecture  Gothic Style  Began in 12th century France  spread quickly until 16th century in Western Europe  Cathedrals – Popular during Gothic Era: “The mighty

cathedral is a symbol of god, his power, and how much people respect him.” (Perdrixet & Krahenbuhl, 1990).  Built vaulted roofs to prevent fires from spreading  Supported building  Columns  Flying buttress – jetted out of wall to serve as support  Roofs  Very tall, pointed structures supported by wood  Have figurines, mostly gargoyles  Made of limestone  Have stained glass windows

Notre Dame Tall vaulted roofs prevents fires

Columns

Stain glass windows

Flying buttress For support

Mathematics in European Architecture  Antonio Gaudi is a Spanish architect who studied

organic geometry in nature and expressed it in his architectural works.  First to use catenary curves in architecture, which

engineers use today to construction suspension bridges

Golden Gate Bridge San Francisco Casa Mila

Sagrada Famillia – represent trees in forest

Mathematics in European Architecture  Antonio Gaudi is a Spanish architect who studied

organic geometry in nature and expressed it in his architectural works. Many types of geometric structuers found in nature:  Hyperboloid (light), helicoid (movement), cone,

matrices  create reeds, bones, trees  First to use catenary curves in architecture which engineers use to construction suspension bridges  Masterpiece: Sagrada Famillia – Church structure built as if in forest

Organic Geometry in Europe  Gaudi, and many other architects are inspired by

nature. Many different types of geometric structures found in nature used in European architecture:  Hyperboloid

Water tower in Russia by Vladimir Shukhov 1896

Organize Geometry in Europe  Helicoids

Vatican Museum Giuseppe Momo in 1932

Staircase actually 2 separate helixes twisting together to make double helix. Just like DNA!

DNA Helicase

Organize Geometry in Europe  Cone

Puglia, Italy

Asian Architecture  Key characteristics are rooftops  Flat, to emphasize the width of the building  All roofs made of gables, similar to shingles  Stresses importance of symmetry  Gardens are asymmetrical to represent nature  Buildings are made from wooden structures because

Asia experiences many earthquakes  Color holds a lot of meaning  Yellow roofs – Imperial/royal color  Blue roofs – Used for religious buildings to symbolize

heaven

 Most imperial buildings face East, direction of sun, as

form of solar worshipping

Mathematics in Asian Architecture  Geometry and art – “Both

concerned with understanding and organization of space” (Gangolli)  Perfected the use of sine, cosine with bridges and large buildings  Abu al-Wafra discovered tangent

and Theory of Parralells

 Patterns  Western Asia uses repetitive patterns that repeat endlessly along a plane 

These types of patterns are commonly used to form basic number of algorithms that can be used for computer generation of patterns.

American Architecture  America is “Melting pot.” Have a lot of other cultural

architecture represented:  Washington Monument – Egyptian obelisk  All types of columns used  Islamic mosques seen in large Muslim populated areas

(NY, Chicago, Los Angeles)  Has cathedrals built in may different parts of America

America has it’s own uniqueness  Chicago 1885: 1st country to build skyscrapers

 California 1944: 1st country to have suburbs

Present day math in Architecture  Mathematics, science, technology and engineering

(STEM) go hand-in-hand with architecture.  Jobs related to STEM and architecture  Engineers  Civil engineers  Interior designers  Landscape Architects  Carpentry

 Industrial design  Building/Private home inspector  Historic preservation  Technical architecture  Construction worker  Electrician

Integrate this into our schools!  K-5  Draw house and room from memory  Perimeter and area  Geometric shapes and patterns  Learn about 2-3D shapes  Learn about history of cities  Design basic floor plans  6-8  Use technology to create 3D floor plans: http://www.architectstudio3d.org/AS3d/home.html  Research historical buildings and “rebuild” them according to modern architectural standards  9-12  Algebra  Advanced geometry  Understand architectural patterns in relation to algebraic and geometric formulas  Trigonometry  Physics/construct buildings  Earth Science: environment and eco friendly homes

The future of Architecture  U.S. Energy Information Administration (EIA)

reported that “in coming years, Building Sector energy consumption will grow faster than that of industry and transportation. Between 2010 and 2030…total Buildling Sector energy consumption will increate by 5.85 QBtu…1 Qbtu is equal to the delievered energy of 37 1000 MW nuclear power plants.” (Architecture 2030, 2011).

The future of Architecture  2030 Challenge:  Eliminate the use of fossil fuel consumption in buildings

Sources  Hendrix, J. (2010). "Architecture as the Psyche of a

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Culture.” School of Architecture, Art, and Historic Preservation Faculty. Clark, K. (1969). Civilisation. New York: New York. Carnegie Museum of Art (1999). The Pritzker Architecture Prize. Pittsburg, PA: Carnegie Museums of Pittsburg. Rossi, Corinna (2004). Architecture and Mathematics in Ancient Egypt. Cambridge: Cambridge University Press. Lohner, F.; Zuberbuhler, T. (2006). Building the Giant Pyramid. Retrieved April 20 from http://www.cheops-pyramide.ch/khufupyramid/pyramid-alignment.html#seked D. Stocks, Manchester Archaeological Bulletin 2 (1987); 49-50, fig. 25. Retrieved April 20 from http://hbar.phys.msu.su/gorm/ahist/arnold/arnold.htm Mashayekh, H. Wisdom in Art: Mathematics in Islamic Architecture in Iran. Retrieved April 20 from http://www.nasrinfoundation.org/doc/Math-Arch.pdf King, D. “Qibla Charts, Qibla Maps, and Related Instruments.” Cartography in Traditional Islamic and South Asian Societies. The History of Cartography, (2), 1. Retrieved April 20 from http://www.pps.k12.or.us/depts-c/mc-me/be-as-ma.pdf

Picture sources  http://www.skyscrapercity.com/showthread.php?t=367782&page   

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=6 http://blog.lib.umn.edu/tangx151/architecture/2008/03/inspirin g_european_architects.html http://the-old-quay-house-fowey.oldhousess.com/americahomes/ http://www.richardcassaro.com/freemasonry%E2%80%99s%E2%80%9Clost-secret%E2%80%9Dfound%E2%80%94encoded-into-the-architecture-of-gothiccathedrals http://library.thinkquest.org/10098/egypt.htm http://www.geometryatlas.com/entries/438 http://atlasobscura.com/blog/spiraling-out-of-control-thegreatest-spiral-stairs-in-the-world