Golden Rectangle Calculator
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Golden Ratio
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About Golden Rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1.618:1. It has been used in art and architecture for centuries due to its aesthetically pleasing proportions.
Golden Ratio (φ)
φ = (1 + √5)/2 ≈ 1.618033988749895...
The golden ratio is an irrational number that appears in many places in nature and art.
Rectangle Dimensions
width/height = φ
In a golden rectangle, the ratio of the longer side to the shorter side equals the golden ratio.
Golden Spiral
The golden rectangle can be divided into a square and a smaller golden rectangle. Repeating this process creates a golden spiral, which appears in nature (e.g., nautilus shell).
Properties
- When a square is removed from a golden rectangle, the remaining rectangle is also golden.
- The golden ratio is the most irrational number, making it difficult to approximate with rational numbers.
- It appears in the Fibonacci sequence and many natural phenomena.