By AGNES PASCO CONATY
As I take in the seasons in my West Laurel backyard, I often think about math— an oak leaf’s balanced symmetry, the triangular shape of a poplar leaf, the perfection of a pine cone’s spiral. Everywhere I look, I see nature’s examples of geometry, symmetry and the visually pleasing golden ratio.
And we humans create and construct on a foundation of math, too. I walk around our neighborhood every day for exercise, and I often take a route that brings me to a traffic roundabout. Walking around that full circle, I’m following its circumference. If I walk from one side of the circle through the center point and straight to the other side, I’m marking the circle’s diameter. And as I walk, I’m thinking about the math under my feet: Dividing the circumference by the diameter, I get the number pi.
Local historic structures — Snowden Hall, at Patuxent Research Refuge, and the Montpelier Mansion come to mind — are excellent examples of bilateral symmetry. If you draw an imaginary line right down the center of either building, the right and left sides are mirror images of each other. And if you wander into Montpelier, you may spot the main staircase’s beautiful bannister, which flows upward from a gracefully spiraling curve designed with mathematical precision.
Courtesy of Joe Murchison
Bilateral symmetry is a mathematical principle that denotes side-to-side sameness — and not only in architecture. This kind of symmetry allows most creatures, from the smallest (think tiny insects) to the largest (dinosaurs!) to move through the air, on land and in water. Bilateral symmetry can create elegance and beauty, too, especially in faces — the exquisitely symmetrical faces of Grace Kelly, Angelina Jolie and Shania Twain all come to mind.
And the golden ratio, another mathematical principle, is all around us, too. This principle, a close relative of the Fibonacci sequence, defines the balance of elements, say parts of a line, that is most pleasing to the eye. (For more on the ratio, go to tinyurl.com/ycynnjyu). Euclid offered the first known description of the golden ratio around 300 BCE, and artists and architects have relied on this principle for centuries. Indeed, Leonardo da Vinci incorporated the ratio in many of his most famous works, including the Mona Lisa and the Vitruvian Man (see more at tinyurl.com/3ase4hdr). And examples of the golden ratio and Fibonacci sequence are abundant in nature, too: the spiral of seeds in a sunflower head (which also captures maximum sunlight), the perfectly arranged chambers of a nautilus shell, a pinecone’s scales.
We can even see the golden ratio in the structure of our own bodies. Take our faces: If you divide the height of your face (chin to the top of your head) by its width, you’ll get a number close to the golden ratio, which is 1.618. The width of your mouth divided by the width of your nose will produce close to this same number. (There are at least two more ways to measure your face that will produce close to the golden ratio, too.) Your arms, hands and fingers also offer examples of the golden ratio — and the structure of our DNA does, too.
As you walk around your own neighborhood, you can be on the lookout for these principles of math, just like I am. Look for the bilateral symmetry that allows your neighbor’s cat to move effortlessly through tall grass (each blade of that grass has bilateral symmetry, too). Check out the symmetry in leaves littering lawns. Birds in flight, falling maple seeds, that squirrel jumping from limb to limb, high in a tree: All of these movements demonstrate mathematical principles.
And if Mother Nature showers us this winter with her magical math miracle, the snowflake, we’ll be playing in fractals, the repeating pattern of hexagonal shapes that make every single flake unique. And as you fashion the face of your snowman, you have a chance to create bilateral symmetry, right down to that big carrot nose!
