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Facial symmetry has a direct relationship to perceived beauty. A guiding approach to facial rejuvenation and balancing facial symmetry is through an application of the golden ratio. [2] Artists and architects have been using this ratio to create works that are pleasing to the eye for centuries. [3]
The golden ratio, also known as the golden proportion, was considered the perfect measurement of harmony, beauty and proportion in Ancient Greece. Researchers Mohammad Khursheed Alam, Nor Farid Mohd Noor, Rehana Basri, Tan Fo Yew and Tay Hui Wen conducted a study to test if the golden ratio was a contributor to perceptions of facial ...
The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
It has been suggested that the ideal human figure has its navel at the golden ratio (, about 1.618), dividing the body in the ratio of 0.618 to 0.382 (soles of feet to navel:navel to top of head) (1 ⁄ is -1, about 0.618) and Leonardo da Vinci's Vitruvian Man is cited as evidence. [23]
Other scholars question whether the golden ratio was known to or used by Greek artists and architects as a principle of aesthetic proportion. [11] Building the Acropolis is calculated to have been started around 600 BC, but the works said to exhibit the golden ratio proportions were created from 468 BC to 430 BC.
The rectangles chosen as "best" by the largest number of participants and as "worst" by the fewest participants had a ratio of 0.62 (21:34). [20] This ratio is known as the "golden section" (or golden ratio) and referred to the ratio of a rectangle's width to length that is most appealing to the eye. Carl Stumpf was a participant in this study.
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Adolf Zeising (24 September 1810 – 27 April 1876) was a German psychologist, whose main interests were mathematics and philosophy.. Among his theories, Zeising claimed to have found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves.