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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), creating aesthetically pleasing proportions found in art, architecture, and nature.
The calculator uses the formula:
Where:
Explanation: This formula calculates the diagonal length based on the area of the golden rectangle, utilizing the mathematical properties of the golden ratio.
Details: Calculating the diagonal of a golden rectangle is important in design, architecture, and artistic compositions where golden ratio proportions are desired for their aesthetic appeal and mathematical harmony.
Tips: Enter the area of the golden rectangle in square meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is the golden ratio?
A: The golden ratio (φ) is an irrational number approximately equal to 1.618, often found in nature, art, and architecture as a proportion considered aesthetically pleasing.
Q2: How is the golden rectangle defined?
A: A golden rectangle is one whose side lengths are in the golden ratio (approximately 1.618:1), meaning if the shorter side is 1, the longer side is φ.
Q3: Can this calculator be used for any rectangle?
A: No, this formula specifically applies to golden rectangles where the length-to-width ratio equals the golden ratio.
Q4: What are practical applications of golden rectangles?
A: Golden rectangles are used in art composition, architectural design, product design, and web design to create visually appealing proportions.
Q5: How accurate is the golden ratio constant used?
A: The calculator uses φ with high precision (≈1.61803398874989484820458683436563811) for maximum accuracy in calculations.