Golden Ratio Calculator

Discover the beauty of the Golden Ratio (φ) with this interactive calculator. Enter the number of decimal places to explore its approximate value and visual representation.

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Golden Ratio (φ):

What is the Golden Ratio?

The Golden Ratio, often denoted by the Greek letter φ (phi), is an irrational number approximately equal to 1.618. It is defined by the proportion derived from dividing a line segment into two parts such that the ratio of the whole segment to the larger part is the same as the ratio of the larger part to the smaller part. Mathematically, it's expressed as:

$$ \varphi = \frac{a+b}{a} = \frac{a}{b} \approx 1.618 $$

This ratio appears surprisingly often in mathematics, nature, art, and architecture. It's closely related to the Fibonacci sequence, where each number is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5, 8...). As the Fibonacci sequence progresses, the ratio of consecutive numbers approaches the Golden Ratio.

The Golden Ratio is considered aesthetically pleasing and has been used in art and design for centuries, from ancient Greek architecture to Renaissance paintings. Its presence in natural phenomena, like the spiral arrangement of leaves and petals, adds to its mystique and significance.

Sources: Wikipedia, MathWorld