Definition

1. Noun:
   • A specific mathematical ratio: The "golden section" is a special proportional relationship, approximately equal to 1:1.618. It is found when a line is divided into two parts so that the ratio of the shorter part to the longer part is the same as the ratio of the longer part to the whole line.

Examples of Usage

• Noun:
  • The architect used the golden section to determine the most pleasing proportions for the building's facade.
  • Many classical paintings are composed according to the principles of the golden section.
  • The ratio of successive numbers in the Fibonacci sequence approximates the golden section.

Advanced Usage

• "To adhere to the golden section": To strictly follow this proportional rule in design or composition.
  • The layout of the page was carefully designed to adhere to the golden section.
• "Golden section rectangle": A rectangle whose side lengths are in the golden ratio.
  • The shape of many credit cards is close to a golden section rectangle.

Variants and Related Words

• Golden ratio (n): A more common synonym for "golden section," representing the same irrational number, often denoted by the Greek letter phi (φ).
• Divine proportion (n): Another historical name for the golden section.
• Phi (n): The Greek letter (φ) used as a symbol for the golden ratio, approximately 1.618.

Synonyms

• Golden ratio
• Divine proportion
• Mean of Phidias
• Extreme and mean ratio

Related Phrases

• Golden mean: While sometimes used interchangeably, this term more precisely refers to the ethical concept of moderation, but it can contextually relate to the mathematical mean found in the golden section.
• Golden spiral: A logarithmic spiral whose growth factor is related to the golden ratio; it is often constructed using golden section rectangles.

Related Concepts

• Fibonacci sequence: A series of numbers where each number is the sum of the two preceding ones. The ratio of consecutive Fibonacci numbers converges to the golden section.
• Aesthetic proportion: The golden section is frequently cited as a principle of aesthetically pleasing proportion in art, architecture, and nature.

Noun

1. the proportional relation between two divisions of line or two dimension of a plane figure such that short : long :: long : (short + long)