1. What is the Golden Rectangle?

A Golden Rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1.618:1. It 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 Rectangle formula:

Where:

• \( b \) — Breadth of Golden Rectangle (m)
• \( l \) — Length of Golden Rectangle (m)
• \( \phi \) — Golden ratio constant (≈1.618034)

Explanation: Given the length of a golden rectangle, the breadth is calculated by dividing the length by the golden ratio φ.

3. Importance of Golden Rectangle

Details: The Golden Rectangle has significant importance in mathematics, art, architecture, and design due to its aesthetically pleasing proportions that are found throughout nature and human creations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the golden ratio (φ)?
A: The golden ratio is an irrational mathematical constant approximately equal to 1.618034, often denoted by the Greek letter φ (phi).

Q2: Where can golden rectangles be found?
A: Golden rectangles appear in famous architectural works like the Parthenon, in artworks like the Mona Lisa, and in various natural formations.

Q3: What makes the golden rectangle special?
A: When a square is removed from a golden rectangle, the remaining rectangle is also a golden rectangle, creating a recursive property.

Q4: How is the golden ratio calculated?
A: The golden ratio can be calculated as φ = (1 + √5)/2 ≈ 1.6180339887...

Q5: Are there other golden shapes?
A: Yes, there are golden triangles, golden spirals, and other geometric forms based on the golden ratio.