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The diagonal of a golden rectangle is the line segment connecting two opposite vertices. In a golden rectangle, the ratio of length to width equals the golden ratio (φ ≈ 1.618), giving it unique mathematical and aesthetic properties.
The calculator uses the formula:
Where:
Explanation: This formula calculates the diagonal length based on the perimeter while maintaining the golden ratio proportions between the sides of the rectangle.
Details: Calculating the diagonal of a golden rectangle is important in architecture, art, and design where golden ratio proportions are sought for aesthetic harmony. It's also used in mathematical studies of geometric properties.
Tips: Enter the perimeter of the golden rectangle in meters. The perimeter must be a positive value greater than zero.
Q1: What is the golden ratio?
A: The golden ratio (φ) is approximately 1.618, a mathematical constant where the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part.
Q2: Why are golden rectangles considered aesthetically pleasing?
A: Golden rectangles are believed to have proportions that are naturally pleasing to the human eye, appearing in many natural forms and classical art and architecture.
Q3: Can this formula be used for any rectangle?
A: No, this specific formula only applies to golden rectangles where the ratio of length to width equals the golden ratio.
Q4: How is the perimeter related to the diagonal in a golden rectangle?
A: The relationship is derived from the fixed proportion between sides (1:φ) and the Pythagorean theorem applied to the diagonal.
Q5: What are some real-world applications of golden rectangles?
A: Golden rectangles are used in design, architecture (Parthenon), art (Mona Lisa), photography composition, and product design for their harmonious proportions.