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

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

Temple of Luxor

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 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

Temples were built on an 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

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

Al-Quran

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-palladium-

manganese

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

Flying buttress For support

Stain glass windows

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

DNA Helicase Vatican Museum Giuseppe Momo in 1932

Staircase actually 2

separate helixes twisting

together to make double

helix. Just like DNA!

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

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/khufu-

pyramid/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

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