For centuries, a mathematical concept called phi has fascinated artists, architects and mathematicians -- and more recently, readers of "The Da Vinci Code."
It's a ratio, an aesthetically pleasing proportion of one length to another. It's the basis of much of the artwork of Leonardo Da Vinci and Michelangelo, the pattern of many parts of the human body and the reason Athens' famous Parthenon has endured as an architectural icon.
The partners in a Stow, Ohio-based interior redesign company have caught the phi bug, too. In the last year, they've rebuilt their business around the concept and are redecorating clients' homes based on what is sometimes called the golden ratio or golden section.
Their business, Phi Design, specializes in interior redesign, which means partners Elizabeth Feeney and John Hively rearrange the furniture and accessories their clients already own. The twist is that they're marketing their use of math -- specifically, phi -- in figuring out exactly where those items should go.
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Phi, they say, yields interiors that are more calming and inviting than any arrangement they could devise themselves.
"We like to say we take beauty from the eye of the beholder to every eye beholding," said Hively, a retired certified public accountant who is the mathematician to Feeney's designer.
Phi is a highly specific proportion, one our brains are wired to prefer, said Timothy Norfolk, a mathematics professor at the University of Akron, Ohio, with whom Feeney and Hively consulted. "There's something biologically pleasing about these patterns," he said.
Phi shows up frequently in nature as well as in art and architecture. It's the ratio of the length of your forearm to your hand, for example. It's the ratio of the ever-increasing widths of the segments of a spiral seashell. It's the ratio of the width of the Parthenon to its height.
Think the proportions of Michelangelo's "David" are pretty close to perfection? Thank phi.
It's also a concept that interior designers study in their basic course work, said Pamela Evans, coordinator of the interior design program at Kent State University. A good interior designer -- one who's trained in design, not just a decorator -- will incorporate phi into the proportions of a room, she said.
Hively and Feeney use the ratio to calculate the best placement for furniture, pictures and other objects in the rooms they redecorate. They'll measure a distance -- say, the length of a wall -- and then determine what they call the "phi cut," the dividing point where the two sections are in perfect proportion. That's where they'll position an armoire, a chair or some other item.
Feeney, a former designer at Akron's Marvin Interiors, has been involved in interior redesign for three years. (She and Hively previously worked together in Phi Design's predecessor business, Room Renaissance.) Before she came across the concept of phi, she was continually applying her redesign skills to the combined living and dining area in her own condo in Stow, she said.
Even with all that rearranging, though, she said she never could get the feeling of the space quite right.
It wasn't until she and Hively applied phi that the room finally came together. "I haven't moved this furniture for months," she said.
The two started their redesign with a round pedestal table that had belonged to Feeney's aunt, a piece that was important enough to her that she wanted to build the room around it. They measured the distance from one wall to the fireplace hearth, then placed the table at the phi cut between those two points. An armchair went at the phi cut between the round table and the wall. They measured the length of the room; one end of the sofa was positioned at the phi cut of that distance.
And on they went, using phi to position the most important pieces in the room. Then they relied on Feeney's artistic sense to accessorize -- although in some cases, they even used phi for that. A vignette they created on the fireplace mantel out of an old frame and some treasured heirlooms is perfectly proportioned according to phi.
The ratio is unforgiving, Feeney said, because there's only one right dividing point for any given measurement. But in placing a piece, she and Hively often have a number of measurements to choose from, she noted.
If a chair doesn't work at the phi cut of one wall, for example, they might try an adjoining wall. Or perhaps they'll measure the space between two architectural features rather than the entire wall. Often they'll search their clients' homes for items from other rooms they can incorporate, but only if they'll work in the proportions of phi.
Some items, such as pianos, can't be moved to comply. In those cases, Hively and Feeney will put something next to the item in the proper phi position to make the whole composition correct.
One of the reasons phi works, Feeney said, is it results in arrangements with a pleasing kind of asymmetry.
When we look at something, our eye is drawn to what's wrong, she said. So when we look at a symmetrical arrangement, we notice any mistakes that exist.
If what's "wrong" with an arrangement is its asymmetry, however, that's what we notice. And since the arrangement is supposed to be that way, our brain likes what it sees.
Feeney first heard of phi from a friend at her church. She didn't think much about it, though, until the woman sent her the address of a Web site that delved into the concept.
What she learned intrigued her. "It was beyond me," she said, "but I knew it had a place in design."
She and Hively talked to Norfolk, the math professor, as well as to architects, designers and other mathematicians. They spent seven or eight months researching phi before creating Phi Design, a business they introduced at the recent Akron Home & Flower Show.
Feeney has become so adept at using phi that Hively said she can find a correct position for an item almost instinctively. He'll measure, and invariably she'll be within an inch or two of the right spot, he said.
The two are determined to spread the word. Feeney even goes so far as to describe their mission as a calling.
"We're so boring," she said with a laugh, "because that's all we talk about."