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Entering the Nautilus

“In order to understand the universe you must know the language in which it is written and that language is mathematics.”

Galileo Galilei (1564 -1642)

In the year 1202 an Italian mathematician named Leonardo Pisano Bigolio published his Liber Abaci, (The Book of Calculations.) Within that text, Leonardo Pisano Bigolio – aka Leonardo of Pisa – aka Fibonacci, identified a particular sequence of numbers, now referred to as the Fibonacci Sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ………ad infinitum

This simple sequence begins with 0, 1. Each subsequent number is the sum of the two previous numbers. 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, and so on….. When this sequence of numbers is translated into physical geometry, repeated self-similar, expanding patterns are created. The relationship of the numbers to each other in the growth pattern defined by the Fibonacci Sequence approaches what is called the Golden Ratio, an irrational number approximately equal to 1.618.

The growth pattern of the chambered nautilus shell can be described and recreated using the numbers of the Fibonacci Sequence. Illustrating the nautilus spiral begins with plotting equilateral squares defined by the numbers of the Fibonacci Sequence: 1x1, 2x2, 3x3, 5x5, 8x8, 13x13, 21x21….

Drawing a smooth curve through the center of each adjoining, progressively larger square generates the spiral design.

The growth pattern of the chambered nautilus is self-similar; although the size of the nautilus changes, the shape does not. When mathematically comparing any two neighboring chambers of the shell to each other, they are found to be consistently proportionate to one another. The nautilus shell expands at a predictable, measurable rate.

In 1753 Scottish botanist Robert Simson recognized the spiral pattern described by the Fibonacci sequence in the growth of many plants. The spacing of petals on a single rose, the opening of a fern frond, the detail of Romanesco broccoli, the arrangement of leaves on the spiral vera, the pattern of the pinecone - all can be described with the language of mathematics. Amazing!

For centuries this natural symmetrical pattern has been recognized for its profound aesthetic appeal and used in art, architecture, engineering, music, and even web design.

“There is geometry in the humming of the strings, there is music in the spacing of the spheres.” Pythagorus (570 - 495 BCE)

In the spring of 2018 I had the unique opportunity to physically enter the nautilus design. My son Kyle and I visited the Huntington Library and Botanical Gardens in San Marino, California. We were thrilled to discover that our visit overlapped with the temporary installation of the NASA Orbit Pavilion, reconstructed on the Huntington grounds in 2016.

In 2015 NASA commissioned Studio KCA of New York to create a structure that would provide visitors an opportunity to listen in real time to the sounds of satellites orbiting and monitoring the earth. The shape of the structure was inspired by holding a seashell to one’s ear to listen to the sound of the ocean. The soundscape and array of speakers inside the Orbit were created by artist and composer, Shane Myrbeck. The Orbit was originally installed at the 2015 World Science Festival at New York University.

“Satellites that study the earth are passing through space continuously collecting data on everything from hurricanes to the effects of drought. NASA’s Orbit Pavilion sound experience is an outdoor installation that produces an innovative ‘soundscape’ experience representing the movement of the International Space Station and 19 earth satellites. Inside the large, shell-shaped sculpture, distinctive sounds are emitted as each satellite passes overhead: a human voice, the crashing of a wave, a tree branch moving, a frog croaking. Each sound interprets one of the satellites’ missions.”

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1 Comment

At the end of the NASA video there were some terrific links to other videos, including to the Zaha Hadid group's Danjiang Bridge. Fantastic.

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