Dog shows are sometimes criticized as being mere canine beauty pageants, self-aggrandizing spectacles where dogs are paraded around for the chance to win a blue ribbon and a title or two. To the uninitiated, the backstage bottles of hair spray and assorted flat irons certainly seem to suggest that physical beauty – or at least hair dressing – is a consideration when show dogs are presented before the judges.

But what exactly is beauty?

Merriam-Webster defines beauty as “the quality or aggregate of qualities in a person or thing that gives pleasure to the senses or pleasurably exalts the mind or spirit.” This certainly describes the typical show dog (at least in the mind of its proud owner), but it may also apply to the mismarked pet and the lively little mixed breed rescued from the shelter. After all, any dog can lift one’s spirit and, therefore, be described as possessing beauty.

To purebred dog breeders, exhibitors and judges, however, a truly beautiful dog is something more. A great show dog certainly “exalts the mind or spirit,” but it must do so within the often-narrow definition of an ideal as outlined by its breed standard. The qualities that define the show dog’s beauty are both enigmatic and measurable to some degree.

In an article published in the November 2012 issue of Smithsonian Magazine titled, “Beauty by the Numbers,” Dana Mackenzie addresses a surprisingly simple concept: mathematical beauty. The freelance mathematics and science writer claims that mathematical beauty is an “eternal verity” that is not subject to a standard of judgment or criterion for excellence. Beauty is universal, he theorizes, and not a subjective exercise as are the arts and literature, or showing dogs for that matter.

Many breed standards support the mathematics of beauty by providing various measurements for height and weight, ratios for length versus height, and a limit for the number of missing teeth allowed. These figures are based on a breed’s need to perform a specific purpose, whether that’s guarding person and property, dispatching vermin under ground, or retrieving dead and wounded game. Quantifiable measurements, with disqualifications when appropriate, support a mathematical ideal of beauty as it pertains to form and function.

The AKC breed standard for the Weimaraner includes several measurements that help to define this intelligent breed’s ideal state of perfect beauty. Photo © Brian Goodman/Dreamstime.

To illustrate the mathematics of beauty as it pertains to purebred dogs, one need look no further than many of the breeds developed in Germany. The standards for the Dachshund, Rottweiler and Weimaraner, to name a few, can be exacting in their description of the ideal state of perfection for these breeds.

The Weimaraner, for example, is the product of selective 19th-century German breeding to develop its speed, scenting ability, courage and intelligence. The AKC standard for the breed emphasizes its intended purpose as a bird dog and personal hunting companion by including specific measurements for the height at the withers (25-27 inches for dogs and 23-25 inches for bitches), length of ear leather (approximately two inches from the point of the nose), correct scissors bite (upper teeth protruding over the lower teeth by no more than one-sixteenth of an inch) and length of tail (approximately six inches.)

As described by its breed standard, a Weimaraner with a tail too short or long possesses a minor fault. More than four missing teeth is a major fault, as are short ears, and a dog or bitch deviating in height by more than one inch in either direction is to be disqualified. In these four areas, the ideal state of perfect beauty for the breed certainly has a mathematical model.

Of course, few, if any, Weimaraners (or Rottweilers, Dachshunds or any other recognized breed of dog) will measure up to the ideal in all areas, and this is why the breeding and evaluation of purebred dogs is not strictly a mathematical exercise. Many dogs easily satisfy a standard’s rigid measurement requirements, but fall completely short as a whole when it comes to meeting the expectations of an acknowledged breed authority.

Since their inception, dog shows, like beauty pageants, have been peculiar exhibitions in that evaluations are directed by a prescribed standard or protocol, yet decisions are also made by an entirely subjective set of criteria. Contestants may demonstrate perfect measurements, but only a precious few will exalt the mind and spirit of the judges.

The next Miss America and Westminster winners will not be crowned simply because they conform precisely to a specification. Their titles will be won in no small part thanks to an indefinable “something” that no mathematician can quantify and few judges can succinctly define with mere words. At a dog show, beauty is acknowledged with a purposefully pointed index finger. The essence of beauty, after all, can only truly be measured by the admirer’s response to it.