1. What is a Golden Rectangle?

A Golden Rectangle is a rectangle whose side lengths are in the golden ratio (approximately 1.618:1). This proportion has been considered aesthetically pleasing throughout history and appears in many works of art and architecture.

2. How Does the Calculator Work?

The calculator uses the Golden Ratio formula:

Where:

• \( Width \) — The shorter side of the rectangle (any units)
• \( \phi \) — The golden ratio (approximately 1.618)
• \( Length \) — The longer side of the rectangle

Explanation: The golden ratio is an irrational number that appears frequently in geometry, art, and nature.

3. Importance of the Golden Ratio

Details: The golden ratio has been used in design and architecture for centuries, from the Parthenon to modern graphic design. It's believed to create proportions that are naturally pleasing to the eye.

4. Using the Calculator

Tips: Enter the width of your rectangle (must be a positive number). The calculator will compute the corresponding length that creates a golden rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What is the exact value of the golden ratio?
A: The exact value is (1 + √5)/2, which is an irrational number approximately equal to 1.6180339887...

Q2: Can I use any units with this calculator?
A: Yes, the units can be anything (cm, inches, meters, etc.) as long as you're consistent.

Q3: Where does the golden ratio appear in nature?
A: It appears in the arrangement of leaves, flower petals, pinecones, hurricanes, and even in the proportions of the human body.

Q4: What's the difference between a golden rectangle and a regular rectangle?
A: A golden rectangle has sides in the golden ratio proportion, while a regular rectangle can have any length-to-width ratio.

Q5: How is this related to the Fibonacci sequence?
A: The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers get larger.