Final answer:
The Golden Ratio is a principle of balance and proportion found in nature and used in art and architecture, mathematically represented by the ratio Φ ≈ 1.618, observed in galaxies, plants, Greek architecture, and Renaissance art.
Step-by-step explanation:
The Golden Ratio is a mathematical and aesthetic principle which expresses a relationship of balance and proportion, often found in nature and used in art and architecture. In mathematical terms, the Golden Ratio occurs when the ratio of two quantities is the same as the ratio of their sum to the larger of the two quantities, typically denoted by the Greek letter Phi (Φ) which is approximately 1.618. This ratio is achieved when the equation (a+b)/a = a/b is satisfied, where 'a' is larger than 'b'.
Examples of the Golden Ratio can be seen in the spirals of galaxies, the pattern of seeds in a sunflower, the proportions in some Greek temples such as the Parthenon, and in the work of artists like Leonardo da Vinci with his Vitruvian Man. The Golden Ratio provides a symmetrical, balanced, and visually pleasing proportion that has been used to achieve beauty and harmony in various fields such as art, architecture, and design.
An investigation of the Golden Ratio's significance in the art world was conducted by Elizabeth Mjelde, who examined whether this ratio was consistently used in the works from different periods exhibited at the Whitney Museum. This exploration highlights the enduring influence of the Golden Ratio in artistic creations throughout history.