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The Golden Proportion: Key To The Secret Of Beauty

机译:黄金比例:美丽秘诀的关键

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The Golden Proportion, a mathematical ratio, represents beauty, harmony and balance in physical form. Over the centuries, this geometric constant has influenced architecture, biological systems, mathematics and art. This ratio is believed to hold the key to the secret of beauty and finds its representation in innumerous natural and manmade masterpieces. The paper discusses various aspects of this ratio and their relevance in human aesthetics. Introduction The Golden Proportion (Ф) has been known as mathematics of harmony since antiquity. This is believed to be a blueprint for features in nature, art, architecture and humans that conform to harmony and beauty.[1],[2],[3],[4] This proportion encompasses both organic and inorganic entities and has been found represented in numerous natural and architectural marvels ranging from Egyptian Pyramids, famous Greek temple Parthenon, classical work of Leonardo Da Vinci “Mona Lisa” and “Last Supper”, Corbusier human body sketch of proportion “Le Modulor”, musical compositions of Mozart , Beethoven to the human form itself.The Golden Proportion is defined geometrically as the ratios, where the ratio of the whole segment to the longer segment is equal to the ratio of the longer segment to the shorter segment. Mathematically, the precise value of this Ratio is expressed as 1.6180339887..., a never-ending, never-repeating number which goes to infinity. Hence this ratio cannot be expressed as a whole number or as a fraction and is considered an irrational number. Drawing algebraically this ratio, the point C divides the line AB in such a way that the ratio of AC to CB is equal to the ratio of AB to AC. The algebraic calculation shows that the ratio of AC to CB and AB to AC equals 1.618… while the ratio of CB to AC is equal to 0.618…
机译:黄金比例是一种数学比例,以物理形式表示美丽,和谐和平衡。几个世纪以来,这种几何常数影响了建筑,生物系统,数学和艺术。该比例被认为是美丽秘诀的关键,并在众多自然和人造杰作中得到体现。本文讨论了该比率的各个方面及其在人类美学中的意义。简介自上古以来,黄金比例(Ф)被称为和谐数学。据信,这是自然,艺术,建筑和人类中符合和谐与美的特征的蓝图。[1],[2],[3],[4]该比例既包含有机实体,也包含无机实体。被发现存在于众多自然和建筑奇观中,包括埃及金字塔,著名的希腊神庙帕特农神殿,莱昂纳多·达·芬奇的经典作品《蒙娜丽莎》和《最后的晚餐》,比例为“勒莫杜洛”的柯布西耶人体素描,莫扎特的音乐作品,贝多芬与人类的形态本身。黄金比例在几何上定义为比率,其中整个段与较长段的比率等于较长段与较短段的比率。数学上,该比率的精确值表示为1.6180339887 ...,这是一个无穷无尽的无穷大数。因此,该比率不能表示为整数或分数,而被视为非理性数。代数地绘制该比率,点C以AC与CB的比率等于AB与AC的比率的方式划分线AB。代数计算表明,AC与CB之比和AB与AC之比等于1.618…,而CB与AC之比等于0.618…

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