Art, Science, and Mathematics Come Together at Dr. Buchanan Orthodontics

Profiles in Dentistry 2020


Dr. Buchanan Orthodontics Dr. Buchanan Explains the Art of the SmileDr. Buchanan Explains the Art of the Smile

Most people don’t realize how much art, science, and math go into creating an unforgettable and fully functioning smile. Dr. Jennifer Buchanan has made a career out of studying and understanding principles such as the rule of thirds, the golden principle, and the Fibonacci sequence. These aren’t concepts on the radar of the average Dr. Buchanan Orthodontics patient. But that’s okay. All they need to know is Dr. Buchanan can offer them a smile to complement their face, enhance their appearance, and function perfectly.

“There’s a reason we find a particular work of art appealing, a piece of music engaging, or another person attractive,” Dr. Buchanan said. “Although most of us don’t realize why, it has to do with the golden proportion or the golden percentage. In orthodontics, this refers to a mathematical analysis tool we use to analyze the smile and the way it fits into the proportions of the rest of the face. But the principles are first found in nature where they’re referred to as the Fibonacci sequence. It’s actually a mathematic formula (where each number in the sequence is the sum of the two numbers preceding it) found in things like the spiral of a nautilus seashell, the swirl of a hurricane, the flowering of an artichoke—and the structure of the human face. All these things in nature can be enjoyable to look at, even if we don’t understand why we enjoy them. In fact, another name for the Fibonacci sequence is ‘nature’s code’.”

 Dr. Buchanan Orthodontics Dr. Buchanan Explains the Art of the Smile Fibonacci Sequence in Art

The Fibonacci sequence plays an important role in the art world, too. For centuries, we’ve pondered what it is about the face of the Mona Lisa that makes her so enchanting. In fact, it can be explained by The Fibonacci sequence which was also the inspiration for Leonardo DaVinci’s iconic Vitruvian Man. From the Renaissance on, artists like DaVinci have employed the Fibonacci sequence and the golden ratio—whether on purpose or by instinct—to create paintings, sculptures, and photographs that appeal to the human eye. Interior designers use it when designing a space, planning a garden, or even decorating a Christmas tree.

Golden Ratio in Music

Composers and creators of musical instrument have been using these principles for centuries to compose and create music. Mozart based many of his works on the golden ratio, especially his piano sonatas. Antonio Stradivari, creator of violins that now sell for millions, employed the principles of the Fibonacci sequence to create his instruments. The same principles are used today to design saxophone mouthpieces, speaker wires, the acoustic design of cathedrals, and even Lady Gaga says she uses it in her music.

Fibonacci and Orthodontics

“Everything in life—and dentistry—uses symmetry and balance to create what’s beautiful to the human eye,” Dr. Buchanan said. “Artists came to realize that by balancing the features of an image by thirds rather than strictly centering them, their artwork had a more pleasing flow, making it more appealing to the human eye. These numerical patterns have also become an invaluable tool in dentistry. Studying and understanding them helps me design smiles that follow the beauty, balance, and symmetry found in nature. I pay close attention to the same rule of thirds—viewing the patient’s face in three distinct but complimentary regions—to create a smile that’s beautiful within the proportions of that unique face. It’s math. It’s science. It’s art. And the result is a more beautiful you.”

 Dr. Buchanan Orthodontics Dr. Buchanan Explains the Art of the Smile
Art Courtesy of Bradley Donaldson of the Last Art Gallery

Your Safety Comes First

With everything going on right now, Dr. Buchanan wants her patients to know she and her team are taking extra precautions to keep them safe. “We’ve always adhered to OSHA guidelines and have gone that extra mile to keep our office sanitary and our patients healthy. We’ll continue to do everything we can to make your trip to Dr. Buchanan Orthodontics as healthy and safe as possible.”

Cutting-edge Care

Since 1996, Dr. Jennifer Buchanan has pioneered the latest in orthodontic technique and technology for adults and kids. She was one of the first in this area to offer Insignia Customized Braces. Unlike traditional braces which are manufactured to fit any teeth, Insignia braces allow Dr. Buchanan to precisely calculate and apply braces and brackets to affect tooth movement in the most optimal way for each individual patient.

And her advanced 3D technology allows her to show her patients the exact results they can expect before braces ever go on their teeth. She also specializes in the Damon System which allows alignment of teeth without the need to remove permanent teeth or utilize palate expander appliances, improving the overall facial result of each patient for a full, natural 10-tooth smile. Additionally, Dr. Buchanan offers the in-office i-CAT Imaging System for 3D images of each patient’s mouth without gooey, messy impressions.

One of the greatest gifts you can give your child, or yourself, is a beautiful, fully-functioning smile. Orthodontic treatment using the Fibonacci and golden ratio principles can help you look your best, improve your self-image, and give you a healthy, full-functioning smile. Call (972) 542-4412 to schedule your free consultation.




6595 Virginia Parkway (located in Adriatica),
Suite 100
McKinney, Texas 75071
(972) 542-4412


By Meredith Knight
Photos by Scott Peek Photography

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