1. What is the Diagonal of Golden Rectangle?

The diagonal of a golden rectangle is the line segment connecting two opposite vertices. A golden rectangle is a rectangle whose side lengths are in the golden ratio (approximately 1.618:1), making it aesthetically pleasing and mathematically significant.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Diagonal of the golden rectangle
• \( \phi \) — Golden ratio constant (≈1.618034)
• \( b \) — Breadth of the golden rectangle

Explanation: The formula calculates the diagonal length based on the breadth of the rectangle and the mathematical properties of the golden ratio.

3. Mathematical Formula

Details: This formula uses 1 constant (φ - golden ratio), 1 function (square root), and 2 variables (diagonal and breadth). The golden ratio φ is approximately 1.61803398874989484820458683436563811.

4. Using the Calculator

Tips: Enter the breadth of the golden rectangle in meters. The value must be positive. The calculator will compute the corresponding diagonal length.

5. Frequently Asked Questions (FAQ)

Q1: What is a golden rectangle?
A: A golden rectangle is one whose side lengths are in the golden ratio (approximately 1.618:1), considered to be aesthetically pleasing.

Q2: Why is the golden ratio significant?
A: The golden ratio appears frequently in nature, art, and architecture, and is considered mathematically interesting due to its unique properties.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact based on the defined golden ratio constant and the input breadth value.

Q4: Can I use different units?
A: Yes, as long as you maintain consistency. If you enter breadth in centimeters, the diagonal will also be in centimeters.

Q5: Where are golden rectangles found?
A: Golden rectangles appear in various architectural designs, artworks (like the Parthenon and Mona Lisa), and even in nature's patterns.