1. What is a Golden Rectangle?

A Golden Rectangle is a rectangle whose side lengths are in the golden ratio (approximately 1:1.618). When a square is removed from a golden rectangle, the remaining rectangle is also a golden rectangle.

2. How Does the Calculator Work?

The calculator uses the golden rectangle formula:

Where:

• \( a \) — Longer side length
• \( b \) — Shorter side length
• \( \phi \) — Golden ratio (≈1.61803398875)

Explanation: The golden ratio (φ) is a mathematical constant that appears in many natural patterns and is considered aesthetically pleasing in art and architecture.

3. Importance of Golden Ratio

Details: The golden ratio appears in art, architecture, nature (like flower petal arrangements), and even financial markets. It's considered the "most pleasing" proportion to the human eye.

4. Using the Calculator

Tips: Enter the length of one side (b) to calculate the corresponding golden rectangle side (a). The golden ratio (φ) is also displayed for reference.

5. Frequently Asked Questions (FAQ)

Q1: What is the exact value of the golden ratio?
A: φ = (1 + √5)/2 ≈ 1.6180339887498948482...

Q2: Where can we find golden rectangles in real life?
A: The Parthenon, Mona Lisa, credit cards, and many modern designs use golden rectangle proportions.

Q3: What's special about the golden rectangle?
A: It's the only rectangle that, when a square is removed, leaves a smaller rectangle of the same proportions.

Q4: How is this different from the Fibonacci sequence?
A: The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers increase.

Q5: Can I use this for design work?
A: Yes, many designers use golden rectangles to create visually harmonious layouts and compositions.