Spirals

spring rollIt is Winter now, but Spring is right around the corner. Looking back at this picture of a tulip, unfurling from the ground in front of my house a few Aprils ago, got me thinking about spirals.

Many living things, both plants and animals, share this form in their growth patterns. Haeckel_Ammonitida

This plate from Art Forms of Nature  by German biologist Ernst Haeckel shows examples of ancient Ammonitida shells. I marvel at their complexity and perfection.

No less amazing is M74, the Perfect Spiral Galaxy, a spectacular example of a “grand design spiral galaxy.”

m74_baixauli_900

Fibonacci numbers describe these spiral phenomena mathematically.

Fibonacci_spiral_34.svg

There are many works of architecture based on the spiral, from whole buildings to details, to spiral staircases.

There is a special spiral staircase in Baker Hall, at my alma mater, Carnegie-Mellon University (CMU), built with nothing but layered thin Terra-cotta tiles, as a variation of timbrel vault type of construction.

2012_11_12_images_10_guastavini

It supports itself without a steel armature, posts or beams.  The sinuous gentle curve is gorgeous. The a herringbone tile pattern along the curved underside is one of three layers of tile adhered together with fast-setting mortar.  The resulting laminated shell is almost as strong as reinforced concrete.

It was built by the company of a Spanish master builder, Rafael Guastavino, who excelled at designing and building timbrel arches, vaults, and spiral stairs. Guastavino structures, unlike Roman arches and vaults, don’t require heavy wooden supports (centering) during their construction. “The Guastavino craftsmen could start at the four walls of a room and build toward the center. The masons could stand on a ladder or a platform, but they didn’t have to build a wooden frame to support their structure while it was being built—it almost seems miraculous…We have a difficult time today calculating the geometries of (this) structure. I have students here at MIT doing doctoral research, trying to understand how these structures stand up. We can’t build this staircase today.””

The above quote is from MIT structures Professor John Ochsendorf in “Vaulting Ambition,” by Craig Lambert, in Humanities Magazine, a great article that explores the Guastavino’s history, work and influence.

There is an upcoming exhibit in the National Building Museum, called Palaces for the People: Guastavino and America’s Great Public Spaces, which will be on view from March 16, 2013 to January 20, 2014. I hope to get a chance to see it.

The first photo is mine; the second photo is courtesy of Wikimedia Commons; the third photo is courtesy of NASA; the fourth photo is courtesy of Wikipedia; and the fifth photo is courtesy of Michael Freeman.

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2 thoughts on “Spirals

  1. Nice, very nice……..inspiring photos, especially the tile spiral staircase and the M74 perfect spiral galaxy and the simple magnificent beauty of the garden tulip. Many Thanks for sharing these, its helpful to take our mind off of the craziness of “T”. Ian

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  2. A good post for a new year – spirals are optimistic. Next time you are in the grocery store check out the broccoli for a small new growth – it shows a spiral fractal pattern all the way into the smallest form.

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