1. What is the Golden Rectangle?

A Golden Rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618. It's considered aesthetically pleasing and appears frequently in art, architecture, and nature.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( b \) — Breadth of Golden Rectangle (m)
• \( A \) — Area of Golden Rectangle (m²)
• \( \phi \) — Golden ratio constant (≈1.618)

Explanation: The formula calculates the shorter side (breadth) of a golden rectangle when the total area is known, using the mathematical relationship between the golden ratio and rectangle dimensions.

3. Importance of Golden Rectangle Calculation

Details: Calculating golden rectangle dimensions is important in design, architecture, and art where aesthetic proportions are desired. It helps maintain the golden ratio in various applications.

4. Using the Calculator

Tips: Enter the area of the golden rectangle in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

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 ratio related to the golden rectangle?
A: In a golden rectangle, the ratio of the longer side to the shorter side equals the golden ratio (φ ≈ 1.618).

Q3: What are some real-world applications of golden rectangles?
A: Golden rectangles appear in famous artworks, architectural designs (like the Parthenon), product designs, and even in the proportions of credit cards.

Q4: Can I calculate the length if I know the breadth?
A: Yes, the length would be the breadth multiplied by the golden ratio (φ ≈ 1.618).

Q5: Is the golden ratio exactly 1.618?
A: No, the golden ratio is an irrational number (1 + √5)/2, approximately 1.6180339887..., with infinite non-repeating decimal places.