["Golden proportion" and its application to calculate dentition].
Within an evolutionary process, the nature has created the standard of aesthetics - a "gold proportion" on the basis of which, the parts of human body, to be more exact, teeth and denture correspond to each other and to own parts by the size, which is the ideal precondition for ideal appearance. The charming smile serves as the proof, that teeth in denture are located by a principle of "gold proportion". A "gold proportion" is the corner stone of beauty and it can be applied with success in stomatology. Proportion is the certain ratio between parts, and proportional means a proper correlation of parts among themselves. It is reputed, that knowledge about "gold proportion" Pythagor has got from products of the Egyptian and Babylon scientists. And this is true, proportions of cult constructions, bas-relieves, pyramids in Giza, home appliances and ornaments from Tutanhamon tomb testify, that under their creation the Egyptian masters were guided by a principle of "gold proportion". The facade of ancient Greek temple Parthenon is built by a principle of "gold proportion". During archeological digs of this temple the compasses which sculptors and architects of an ancient world used has been found. The "gold proportion" is mentioned in the work which has reached us "Beginning" the author is the scientist of antique epoch Euclid. In 1509, in Venice the book of Luka Pacholi the "Divine proportion" has been published, its illustration is attributed to Leonardo de Vinci. This work has been recognized as a "Hymn of a gold proportion". In 1885 the German researcher professor Zeising published his work - "Aesthetic researches". When Zeising has received numerical values of piece length, he saw that they coincided with figures of some numerical sequence, which was offered by the great Italian mathematician of Middle Ages Fibonacci (or Leonardo Pisano). In his composition the "Abacus Book" Leonardo Fibonacci showed aforesaid sequence of numbers, by means of which he has explained the formula of duplication of rabbits. The specified sequence scientists have seen in many phenomena of the Universe. In sequence of Fibonacci, in some division of its term on previous, it is received irrational number 1,61803398875.., known as Fibonacci. It is used in the reduced, approximated kind as F = 1,618 or phi = 0,618. Fibonacci also gave a proportional number (...3:2, 5:3, 8:5, 13:8...), where numerator represents the sum of two previous numbers in Fibonacci sequence. And in proportional number, similar to numerical sequence, the result of any ratio will be approximately the same - this an irrational number which asymptotically comes to 1,61803398875.... Two numbers of Fibonacci sequence F = 1,618 or phi = 0,618 or phi = 1:F... represent constants of the same sequence. It is actual in stomatology to use proportional way. For example, in orthopedic stomatology taking into consideration of ratio 5:3, promotes improvement of basic fabrics tension, prolongation of teeth functioning and denture, and also planning of correct redistribution of chewing function. In 60th -70th years the American stomatologists carried out many researches to define what kind of part "gold proportion" takes in this area of medicine. Orthodontist Robert Rikets has established that separate teeth correlate with each other by a principle of "gold proportion". In his works Roberts Rickets has specified, that mentioned data is necessary to be considered in aesthetic stomatology during teeth reconstruction. An eminent stomatologist from California, the surgeon, doctor Shtefan Markvart has found out that the height of lateral incisors corresponds to width of lateral incisors by a principle of "gold proportion". This fact has helped the decision of many aesthetic problems. Knowing the width, it is easy to calculate the height and vice versa. When the width is optimum, it cannot be broken with the purpose of closing of an interval. The principle of "gold proportion" in connection with a denture consists in the following: the central incisors are hardly longer than lateral incisors and are almost equal to the length of canines: and lateral incisors are slightly shorter and thinner than the central incisors. The width and the length of each tooth is measured by compasses and calculated for each patient individually. According to a "gold proportion" fore-teeth as a part of person appearance are in the certain ratio to each other. The basic key for the description and construction of four incisors and two canines considers the size (which is accepted as unit) of the width of a small piece of teeth arch or a lateral incisor. On the basis of a lateral incisor width, by the formula of "gold proportion", it is formed the width of the central incisors and canines, and also the length of a fore-part of a dental arch, and vise versa if the length of a fore-part of a dental arch is known, to achieve an ideal aesthetic condition by a principle of "gold proportion", it is defined the width of all fore-teeth. Teeth measurement is taken to define an initial condition, denture calculation, verification of the received results during teeth construction and estimation of the complete denture reconstruction.
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D003817:Dentition; D049669:History, 16th Century; D049672:History, 19th Century; D006801:Humans; D008433:Mathematics; D009811:Odontometry / Q000266:history* / Q000379:methods*