Dr. Levin's golden grid.

A mathematical gauging of a smile

by Alice Shirrell Kaswell, Improbable Research staff

Dr. Eddy Levin of Harley Street puts a golden ratio, not just golden teeth, into his patients’ mouths. Dr. Levin has been at this for a while. It was he who in 1978 wrote a study called “Dental Esthetics and the Golden Proportion,” which graced pages 244–52 of that year’s September issue of The Journal of Prosthetic Dentistry.1

The golden ratio is a special number that has caught the eye and imagination of mathematicians, of artists, and now, thanks to Dr. Levin, of dentists. Some call it the “golden mean” (philosophers, though, use that phrase to mean something else). Some call it the “golden section.” Some Germans call it, evocatively, the “goldener Schnitt.” Almost everyone calls it beautiful.

The golden ratio is the number you get when you compare the lengths of certain parts of certain perfectly beautiful things (among them: snail shell spirals, the Parthenon in Athens, and Da Vinci’s painting “The Last Supper”). You’ll find that the ratio of the bigger part to the smaller equals the ratio of the combined length to the bigger. That ratio, that number, is always the same, ever so slightly bigger than 1.6180339.

If doing sums causes you pain, just go find someone who has perfect teeth and who won’t mind you staring into his or her mouth.

Dr. Levin explains on his website2 that many years ago he was both studying math and trying to find out what made teeth look beautiful. “It was at a moment,” he writes, “like when Archimedes got into his bath, that I suddenly realized that the two were connected — the Golden Proportion and the beauty of teeth. I began to put this into practise and started testing my ideas on my patients. My first case was a young girl in a hospital, where I was teaching, whose front teeth were in a terrible state and needed crowning. Despite the scepticism of the other members of staff and the unenthusiastic technicians with whom I had to work and whose co-operation I depended upon, I crowned all her front teeth, using the principles of the Golden Proportion. Everybody, including the young lady herself, agreed that her teeth now looked magnificent.”

Most important, in Dr. Levin’s reckoning, is the simple tooth-to-tooth ratio: “The four front teeth, from central incisor to premolar are the most significant part of the smile and they are in the Golden Proportion to each other.”

Dr. Levin created an instrument called the “golden mean gauge.” Made of stainless steel 1.5 millimeters thick, and retailing for £85, it shows whether the numerous major dental landmarks “are in the Golden Proportion,” and it is suitable for autoclaving.

Dr. Levin also offers a larger version that is “useful for full face measurements” and “useful to measure larger objects or bigger pictures of furniture etc.”

(Thanks to Stanley Eigen for bringing this to our attention.)

### References

1. “Dental Esthetics and the Golden Proportion,” E.I. Levin, Journal of Prosthetic Dentistry, vol. 40, no. 3, September 1978, pp. 244–52.

2. Golden Mean Gauge

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The article above is from the May-June 2009 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!

Visit their website for more research that makes people LAUGH and then THINK.

The single most important determinant of tooth beauty is their presence. Then let's worry about ratios.
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The women in the lower photo should get her teeth cleaned.
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Interesting. Takes me back to an art class I had in college. The professor espoused the golden triangle for facial features. The measurement from the outside of the left eye to the outside of the right eye and from the outside of each eye to the bottom lip formed an equilateral triangle.
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