In the December 2013 online edition of Discover Magazine, an article written by physicist and cosmologist Dr. Max Tegmark proposes that “everything in the universe is made of math.”

I’m not a mathematician. Finding math challenging I gravitated toward history and geography in college. So, while most of Dr. Tegmark’s article sailed over my head, I did get the gist that there is mathematics in nature, everywhere we look, even if we don’t necessarily recognize it as such at the time. Now, that, I understand.

Rockport, Texas © Rex Vogel, all rights reserved

As a photographer, I look through my camera’s viewfinder and use math to compose visually and see natural and man-made objects in the form of geometry. My eyes are grabbed by circles, angles, lines, arcs, ellipses, rays, and spirals created by beaches, bridges, rivers, rock formations, trees, canyons, waterfalls, and other things I see in the landscapes around me.

Monahan Sands State Park, Texas © Rex Vogel, all rights reserved

The rule of thirds and golden ratio both use mathematics to achieve appealing photo compositions.

Corpus Christi, Texas © Rex Vogel, all rights reserved

The rule of thirds states than an image is most pleasing when its subjects or regions are composed along imaginary lines which divide the image into thirds—both vertically and horizontally. The rule of thirds divides a photograph into vertical and horizontal thirds. Important compositional elements are placed at the intersection of the vertical and horizontal lines.

Bernstein Forest, Kentucky © Rex Vogel, all rights reserved

The golden ratio is an ancient mathematical concept used to design everything from the pyramids in Egypt to photographs in popular fashion magazines. The ratio is 1:1.618.

McAllister Covered Bridge, Parke County, Indiana © Rex Vogel, all rights reserved

Also known as the Golden Mean, Phi, or Divine Proportion, this law was made famous by Leonardo Fibonacci around 1200 A.D. He noticed that there was an absolute ratio that often appears throughout nature, a sort of design that is universally efficient in living things and pleasing to the human eye.

Kentucky Artisan Center at Berea © Rex Vogel, all rights reserved

Since the Renaissance, artists and architects have designed their work to approximate this ratio of 1:1.618. It’s found throughout the Parthenon, in famous works of art like the Mona Lisa and the Last Supper, and it’s still used today.

Great White Egret at Corkscrew Sanctuary, Florida © Rex Vogel, all rights reserved

It is actually quite amazing that a rule so seemingly mathematical can be applied to something as varied and subjective as photography. But it works, and surprisingly well. The rule of thirds is all about creating the right aesthetic trade-offs. It often creates a sense of balance—without making the image appear too static—and a sense of complexity—without making the image look too busy.

Cathedral of St. John the Baptist, Savannah, Georgia © Rex Vogel, all rights reserved

I use that geometry to create scenic images filled with natural frames, leading lines, and orderly or abstract patterns. When you compose a landscape photo, you probably don’t realize you may have chosen that scene based upon geometry. You just know there is something about that landscape catching your attention and worthy of a spot on your memory card.

Lynx Lake near Prescott, Arizona © Rex Vogel, all rights reserved

Bryce Canyon National Park screams large-scale geometry with its arc-shaped scoops of land. As I stood at the view area at Sunrise Point, I noticed the triangle created by the tree trunk and the hanging branches and included them in the composition. In retrospect, I could have used a slightly wider angle to include more of the tree.

Bryce Canyon National Park © Rex Vogel, all rights reserved

Featuring similar geometric shapes, Cedar Breaks National Monument sits at over 10,000 feet and looks down into a half-mile deep geologic amphitheater.

Cedar Breaks National Monument © Rex Vogel, all rights reserved

Arches National Park has over 2,000 natural stone arches, in addition to hundreds of soaring pinnacles, massive fins, and giant balanced rocks. This red-rock wonderland will amaze you with its formations and inspire you with its sunsets.

Arches National Park © Rex Vogel, all rights reserved

Natural Bridges National Monument features three majestic natural bridges that invite the viewer to ponder the power of water in a landscape usually defined by its absence.

Natural Bridges National Monument © Rex Vogel, all rights reserved

The landscape in these Utah parks may seem static but the powers of wind, water, and time constantly sculpt new worlds. Arches and bridges are both fragile, natural rock sculptures. Both are formed with water and time but with different processes. Seeping moisture and frost shape arches while running water carves natural bridges.

Capitol Reef National Park © Rex Vogel, all rights reserved

Go back and look at landscape images you’ve captured. Do you see the natural geometry in your photo compositions? You’ve actually seen and photographed the mathematics of nature.

Monument Valley © Rex Vogel, all rights reserved

Worth Pondering…

The more one looks, the more one sees. And the more one sees, the better one knows where to look.

—Tielhard Chardin