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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
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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
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http://www.geometryatlas.com/entries/438
http://atlasobscura.com/blog/spiraling-out-of-control-thegreatest-spiral-stairs-in-the-world