gold ratio,

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✍️ Ai批改: The term Gold Ratio typically refers to the Golden Ratio, which is a mathematical concept often found in nature, art, and architecture、The Golden Ratio is approximately equal to 1.618033988749895 and is represented by the Greek letter phi (φ).

Key Points about the Golden Ratio:

1、Definition: Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

Mathematically, if \(a\) is the larger quantity and \(b\) is the smaller quantity:
\[
\frac{a + b}{a} = \frac{a}{b} = \phi
\]
where \(\phi\) is approximately 1.618.

2、Geometric Representation: It can be seen in the construction of a golden rectangle, where the ratio of the longer side to the shorter side is the golden ratio.

3、Historical Significance: The ancient Greeks used the golden ratio in their art and architecture, believing it to be aesthetically pleasing、Examples include the Parthenon in Athens.

4、Nature and Biology: The golden ratio appears frequently in nature, such as in the arrangement of leaves on a stem, the spiral of shells, and even in the proportions of the human body.

5、Art and Design: Many artists and designers use the golden ratio to create compositions that are visually appealing、Examples include Leonardo da Vinci's Vitruvian Man and Salvador Dali's The Sacrament of the Last Supper.

6、Mathematical Properties: The golden ratio has many interesting mathematical properties, including its connection to the Fibonacci sequence, where each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13, ...)、As you move further along the sequence, the ratio of successive numbers approaches the golden ratio.

If you have any specific questions or need more details about the golden ratio, feel free to ask!