Vadachkoriia N R, Gumberidze N Sh, Mandzhavidze N A
Georgian Med News. 2007 Jan(142):87-94.
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.
在进化过程中，大自然创造了美学标准——“黄金比例”。基于此，人体各部分，更确切地说是牙齿和牙列，在尺寸上相互对应且与自身各部分相匹配，这是拥有理想外观的理想前提。迷人的微笑就是证据，表明牙列中的牙齿是按照“黄金比例”原则排列的。“黄金比例”是美的基石，在口腔医学中也能成功应用。比例是各部分之间的特定比率，成比例意味着各部分之间相互有恰当的关联。据说，毕达哥拉斯关于“黄金比例”的知识得自埃及和巴比伦科学家的成果。的确如此，宗教建筑、浅浮雕、吉萨金字塔的比例，以及图坦卡蒙墓中的家用电器和装饰品都证明，埃及工匠在创作时遵循了“黄金比例”原则。古希腊帕台农神庙的正面就是按照“黄金比例”原则建造的。在对这座神庙的考古发掘中，发现了古代世界的雕塑家和建筑师使用的圆规。在流传至今的著作《几何原本》中提到了“黄金比例”，其作者是古代的科学家欧几里得。1509年，卢卡·帕乔利的《神圣比例》在威尼斯出版，其插图作者是列奥纳多·达·芬奇。这部作品被视为“黄金比例的颂歌”。1885年，德国研究员蔡辛教授发表了他的著作——《美学研究》。当蔡辛得到线段长度的数值时，他发现它们与中世纪伟大的意大利数学家斐波那契（或莱昂纳多·皮萨诺）提出的某个数列的数字相符。在他的著作《算盘全书》中，莱昂纳多·斐波那契展示了上述数列，借助它解释了兔子繁殖的公式。科学家们在宇宙的许多现象中都发现了这个特定数列。在斐波那契数列中，其某一项除以它的前一项，会得到无理数1.61803398875……，被称为斐波那契数。它以简化的近似形式F = 1.618或φ = 0.618使用。斐波那契还给出了比例数（……3:2、5:3、8:5、13:8……），其中分子是斐波那契数列中前两个数字的和。并且在比例数中，类似于数字序列，任何比例的结果都将大致相同——这是一个渐近于无理数1.61803398875……的无理数。斐波那契数列中的两个数F = 1.618或φ = 0.618或φ = 1:F……代表同一数列的常数。在口腔医学中采用成比例的方法是很实际的。例如，在口腔矫形学中，考虑到5:3的比例，有助于改善基本组织的张力、延长牙齿和牙列的功能，以及规划咀嚼功能的正确重新分配。在20世纪60至70年代，美国口腔医学家进行了许多研究，以确定“黄金比例”在该医学领域中所起的作用。正畸医生罗伯特·里克茨确定，单个牙齿之间按照“黄金比例”原则相互关联。在他的著作中，罗伯特·里克茨指出，在牙齿重建的美学口腔医学中必须考虑上述数据。加利福尼亚的一位杰出口腔外科医生斯特凡·马克瓦特发现，侧切牙的高度与侧切牙的宽度按照“黄金比例”原则相对应。这一事实有助于解决许多美学问题。知道宽度后，很容易计算出高度，反之亦然。当宽度最佳时，不能为了关闭间隙而破坏它。与牙列相关的“黄金比例”原则如下：中切牙几乎不比侧切牙长，且几乎与尖牙长度相等；侧切牙比中切牙稍短且稍窄。每个牙齿的宽度和长度用圆规测量，并为每个患者单独计算。根据“黄金比例”，前牙作为人外貌的一部分，相互之间存在特定比例。描述和构建四颗切牙和两颗尖牙的基本关键是考虑一小段牙弓宽度或侧切牙宽度的尺寸（将其作为单位）。根据侧切牙宽度，通过“黄金比例”公式，可得出中切牙和尖牙的宽度，以及牙弓前部的长度，反之，如果知道牙弓前部的长度，为了通过“黄金比例”原则达到理想的美学状态，可确定所有前牙的宽度。进行牙齿测量是为了确定初始条件、计算牙列、在牙齿构建过程中验证所得结果以及评估全口义齿重建情况。
