Architecture
Under Construction

Spiral Walkway
Spiral Walkway at the Niemeyer Museum of Contemporary Arts, Rio De Janeiro, Niteroi, Brazil
Frank Lloyd Wright designed the Guggenheim Museum based on the proportions of the Japanese Miracle Shell
(Thatcheria mirabilis)

Vor Frelsers Kirke
Copenhagen, Denmark
http://www.vorfrelserskirke.dk/side/2#Architecture
The Great Minaret of Samarra
Iraq, 9th century

The immense brick minaret of the Great Mosque is called the Malwiya, which in Arabic means snail-shell.  
The Great Mosque of Samarra was at one time the largest mosque in the world. Its minaret, the Malwiya Tower, is a vast spiraling cone.  Pilgrims can ascend the tower by the spiral ramp that winds around and to the top of the minaret. Malwiya means snail shell in Arabic.

Read more about the mosque at: 
http://www.dur.ac.uk/derek.kennet/mosque.htm
Making the Metaphysical Physical
It is no accident that the forms from which we derive the most meaning are also the forms most used and most useful in the natural world and, by imitation, in the world of human design.

“Architecture gives form to the invisible pulses and rhythms of life. It gives pattern to structure and structure to pattern. It is an elemental mystic power that is innate to all things. The physical manifestation of this power is a consequence of the desire for the invisible to be made visible. This desire, this great motivating force is essential to the life of a thing. It is a process which organizes and composes various interrelated forces into a unified whole. Architecture is the comprehensive expression of all science and art—the wellspring of interconnectedness and functional art.”

Eugene Tsui
from Evolutionary Architecture

"What we must know in organic architecture is not found in books. 
It is necessary to have recourse to Nature with a capital N in order to get an education.  Necessary to learn from trees, flowers, shells - objects which contain truths of form following function.  If we stopped there, then it would be merely imitation.  But if we dig deep enough ... we arrive at secrets of form related to purpose that would make of the tree a building and of the building a tree."
Frank Lloyd Wright

Building with Spirals

The curves and swirls of shells have inspired architects across the globe. Architects frequently take inspiration from forms in nature.  Both architects and engineers study natural structures in order to learn nature’s building secrets. As we can see, the strength, versatility, and visual appeal of the spiral have made it a common prototype for architectural design.
Tatlin's Monument to the Third International
This spiral iron framework was to support the construction of an elaborate monument designed to have three, independently rotating towers.

Church Spires

Christian churches are often adorned with tapering conical, and sometimes spiral, steeples. Here, the spire has metaphorical purposes: it calls the faithful to worship, and it reaches up toward the divine.  The root of the word spire comes from the Anglo-Saxon word spīr, which means both spear and sprout.  Similar to the conch in many Eastern religions, the church spire represents both the holiness of first creation (as in a plant’s emerging sprout) and military might (as in the holy spear of the Church).
The Reichstag Dome
Berlin, Germany
One of the most striking features of the Swiss Re Tower is the spiral pattern that ascends its curved sides.  This effect is achieved by the slight rotation of each floor relative to the floor below it. The rotation has an ecological as well as a design function in that it creates pressure differentials between the floors that cause air to circulate automatically, thereby reducing the need for air-conditioning and lowering energy consumption.

“New digital technologies make it possible to design and construct buildings like the RE Swiss Headquarters.  Norman Fosters design team developed a special computer program to model the curvilinear geometry of the tower.   Computer modeling technologies have given us the capacity to build using complex curved forms.” 

from Verb Natures
The Swiss Re Tower
Designed by Norman Foster
London, England
The glass Reichstag dome, completed in 1999, is the crowning feature of Berlin’s Reichstag building, home of the German parliament. Following the reunification of Germany, the long-neglected Reichstag underwent restoration, a project directed by architect Norman Foster.  The modernist dome has become a prominent German landmark and a symbol of reunified Germany.

Within the cupola, two steel walkways spiral up the sides of the dome much in the pattern of the double-helix, giving visitors panoramic views of the city. Like the Swiss Re Tower, the Reichstag dome features energy efficient designs as well. A mirrored, conical structure at the center of the dome directs natural light into the building below and also captures solar energy, reducing the building’s reliance on external energy sources.
“It may look like there are infinite patterns in nature and in the human built environment, but this is not the case.  From the smallest organisms to the scale of the universe itself, there are a relatively small number of basic patterns, each of which has a particular function.  The meandering river expresses flow.  Branching patterns in rivers and trees, like the branching design of our body’s circulatory system, express efficient circulation and distribution.  Helixes and spirals, from the organization of DNA to the spiral of a shell or the form of the galaxy itself, all express the dynamic organization of growth.”

Sim Van der Ryn,
Architect
The Vatican Museums'
Spiral Staircase
Designed by Giuseppe Momo, 1932

The broad steps give this structure the feeling of being part ramp and part staircase.
The Tower of Babel
Pieter Brueghel the Elder, 1563

The Tower of Babel is one of the most famous symbols for the yearning to reach god, manifested through the construction of spiral buildings. The demise of the Tower also represents the inescapable forces of dissolution and death that are the fate of all spiral structures—and everything in the universe, for that matter—including the majestic galaxies that spin for billions of years. Everything that spirals eventually spirals out of control.

The Confusion of Tongues
Gustave Doré, France, 1865
It is thought that Doré conceived this representation of the Tower of Babel based on the extant Minaret of Samarra.

The Reichstag Dome
Berlin, Germany

The Golden Ratio

We've discussed the golden ratio in the context of plants and phi as well as in art, but this proportion has played an important role in the history of architecture as well, notably in the Acropolis and the Parthenon.

In modern architecture, Swiss architect Le Corbusier is famous for his devotion to systems of harmony that are closely related to the golden ratio and the Fibonacci series. He described these ideas of mathematical order as "rhythms apparent to the eye and clear in
their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages, and the learned.”

Image from http://commons.wikimedia.org/wiki/File:Kien_truc_symbol.JPG.