Sunday, August 25, 2013

Daniel Acosta on Art and Science: The Golden Ratio

My old Baylor friend Daniel Acosta, who double-majored in biology and English literature, now works as a gastroenterologist in Corpus Christi, Texas, where he often muses on art and science and writes about his musings for a "local medical magazine," the Coastal Bend Magazine, in which he some time ago published a piece titled "The Chambered Nautilus," partly inspired through a trip taken by him and his wife to an isolated bed-and-breakfast place in the Texas Hill Country, where he glimpsed a 'miracle':
One morning as I sat on the porch sipping my coffee, something that lay on the fence caught my eye. It was a beautiful fossilized seashell, a chambered nautilus well preserved by Time's loving hands. The owner of the place told me "Oh yeah, I found those laying around here, I guess this place lay under the sea a long time ago." He kindly gave me one as a gift. When I first held the fossil in my hand I tried to contain my joy, as I wanted to blurt out like Everyman in the old English play and say, "This matter is wondrous, precious!" The chambered nautilus has always fascinated me for its immeasurable beauty, its unique blend of mathematical construct and natural artistry. Now I begin to imagine that this fossil represented the most primordial form of the shell, the Ur-Nautilus itself. Here, despite the layers of millions of years that it had sat on this Central Texas soil, one could make out in its primitive form the wonderful logarithmic spiral that is the mathematical basis of the shell's architecture. I took my treasure home and it now sits proudly on my bookshelf at home next to a modern day chambered nautilus.

The logarithmic spiral of the chambered nautilus is of course one of the most exquisite examples of the Golden Ratio. The Golden ratio is that magical irrational number which is the mathematical basis of the logarithmic spiral that we see in seashells, whirlpools, the spiral construct of a pine cone and the phyllotaxic arrangement of leaves in many plants. The number was first discovered by Euclid in 300 BC when he defined how to divide a line into "the mean and extreme ratio." Namely, that "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater segment to the lesser."


That simply means that the ratio of the line AB to AC is equal to the ratio of AC to CB. The number of this ratio, it turns out is an irrational number with the value of 1.61803 ad infinitum (much like pi is an irrational number of 3.14 ad infinitum). In fact, the Golden Ratio is also called phi (with its corresponding Greek symbol).
The miracle glimpsed was, of course, the spira mirabilis, a fossilized version of the modern-day exemplar that sits on Danny's bookshelf, as depicted in the photo above, which he recently sent me.

I am fortunate to have friends in the sciences with such broad educations as Danny Acosta and, naturally, Pete Hale, both of whom combine art and science in their lives . . .

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At 9:03 PM, Blogger Able said...

I've always found the Fibonacci Numbers to be fascinating (well except when I 'had' to study them).

A couple of links I like:

nice illustrations

and an in-depth explanation beginning from Fibonacci Rabbits

At 9:33 PM, Blogger Horace Jeffery Hodges said...

Let me link:

nice illustrations

in-depth explanation

That's easier . . .

Jeffery Hodges

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