Someone mentioned to me that the nautilus shell is an example of the “golden ratio,” a mathematical ratio based on the number Phi. Phi (with upper case “p,” Greek letter Φ) represents the number 1.618… It’s reciprocal, phi (with lower case “p”, Greek letter φ), equals 0.618… Since math is all Greek to me anyway, it was hard for me to grasp the concept of Phi, but the ratio it represents can be seen in relationships all throughout the universe.
The website GoldenNumber.net explains the ratio in detail (I won’t attempt to do so myself), and gives many examples of how it appears around us: in proportions of the human body, proportions of some animals, DNA, plants, music, art, geometry, the solar system, the movements in the stock market... even in the designs of the Egyptian pyramids and the design of the Star Trek spaceship, the USS Enterprise. And, as noted, in the shape of the spiral of the nautilus shell.
Some people would argue that the application of the golden ratio, in many instances, is based on arbitrary points of proportion that happen to match the equation. Kind of the idea that when all you have is a hammer, everything looks like a nail. If you set about looking for a particular pattern or ratio, you can find ways to fabricate its appearance in almost anything.
In the case of the nautilus shell, the actual shape of the shell approximates the “golden spiral” shape as defined by the golden ratio, but it is not an exact match. GoldenNumber.net tells us that, “There is, however, more than one way to create spirals with golden ratio proportions of 1.618 in their dimensions,” and goes on to demonstrate that the golden ratio can, indeed, be seen in the nautilus shell, just not in the way that is typically – and incorrectly – demonstrated.
But then the plot thickens. According to Wikipedia, while the nautilus shell does not directly correlate to a golden ratio spiral, it is in the form of a logarithmic spiral. The logarithmic spiral, first described by French mathematician Rene Descartes (he called it Spira mirabilis, "the marvelous spiral"), can also be expressed mathematically. I will again defer to the internet to explain the math (I guess in this case, it’s all French to me).
The logarithmic spiral also occurs in many forms in nature. Examples given by Wikipedia: the approach of a hawk to its prey; the approach of an insect to a light source; the arms of spiral galaxies; the nerves of the cornea; the bands of tropical cyclones; patterns in sunflower heads; and, of course, the shells of mollusks (i.e. the chambered nautilus shell).
So what is the significance of all of this? To me it indicates that there is a strong interrelationship between virtually everything in nature (and the aesthetics of some things manmade); that there are forces bigger than we can imagine at work in the universe; and that on some level there is, indeed, a “grand design” to everything. This is, perhaps, where science and religion come together in a very tangible way.
So whether the nautilus depicts a “golden ratio” or a “marvelous spiral,” the bottom line is that it’s a really cool design to have in my stained glass panel. What, you expected something deeper? You’ll have to wait until I brush up on my math. And my Greek.