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  • Terry Wigmore

Fibonacci and the Phi Ratio

The Fibonacci sequence has always been intriguing to me, not in any New Age, dogmatic sort of way, but as a point of intellectual curiosity. I am not a mathematician, and only at times, would I consider myself to be moderately comfortable with any type of exploration of equations. I do love patterns, and recognizing patterns in Nature has brought me great delight, especially as I took up photography.

What I discovered through the lens of my camera were all kinds of patterns easily discernible and accessible to me. I love the Sunflower, their sturdy stems and large heads, but even more interesting to me was the spiral of seeds that emerged as the plants grew larger. Little did I realize that the ability of the Sunflower, to package its seeds in these increasing spirals, was actually a principle of efficiency. How does a plant generate the best reproductive survival rate possible? The answer is by maximizing the number of seeds it can package in the head of the seed pod. That organizational spiral represents a form of the Fibonacci sequence. That beautiful spiral pattern may not be about aesthetics at all. It may be more a statement of how an organism follows the principle of efficiency for the survival of the species. It turns out, survival is a beautiful thing :)

While the Nautilus shell is often used to demonstrate the Phi Ratio (another term for the relationship of the numbers in the Fibonacci sequence where the relationship of 2 numbers in the sequences can be understood as a ratio of the larger number to the sum of the two numbers (a+b:a = a:b = 1.618034 or 1.618), it is not always, and absolutely perfect. I suppose it is just like Da Vinci's Vitruvian Man, it is the idea of perfection in the form, but the reality is more varied. Still, the examples of relationships approximating 1.618 are quite astounding to me. And that is cause to pause and to ponder. Nature speaks, the cosmos speaks and more often than not, that language is Mathematics. When the numbers become patterns and patterns become things I can see (or, in the case of music, things I can hear), I do tend to sit up and take notice. From sea shells to snail shells, sunflowers to pine cones, and bees to spiral galaxies, I think the Universe (and it's Maker?) is speaking, and I had better pay attention.

So, while not being a fanatic about what I observe, I do wish to take some time to poke around ideas in Nature that numbers seem to suggest as being significant. Phi, the Golden Ratio is one of those numbers.

one of my many sunflower photos

one of several shells I have collected illustrating the Phi Spiral

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