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Golden Ratio Formula:
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The golden ratio (φ) is a mathematical constant approximately equal to 1.618. It appears in various natural and designed structures and is often considered aesthetically pleasing.
The golden ratio is calculated using the formula:
This formula derives from the quadratic equation \( x^2 - x - 1 = 0 \), where φ is the positive solution.
Details: The golden ratio appears in mathematics, art, architecture, and nature. It's used in design for creating visually appealing proportions and is found in patterns like the Fibonacci sequence.
Tips: Simply click the "Calculate" button to compute the golden ratio value. No input parameters are needed as it's a mathematical constant.
Q1: What is the exact value of the golden ratio?
A: The exact value is \( \frac{1 + \sqrt{5}}{2} \), which is approximately 1.6180339887...
Q2: Where does the golden ratio appear in nature?
A: It appears in the arrangement of leaves, flower petals, pine cones, and even in the proportions of the human body.
Q3: How is the golden ratio related to the Fibonacci sequence?
A: The ratio of consecutive Fibonacci numbers approaches the golden ratio as the numbers increase.
Q4: Is the golden ratio used in modern design?
A: Yes, it's used in graphic design, photography, architecture, and web design to create harmonious compositions.
Q5: Can the golden ratio be expressed as a continued fraction?
A: Yes, it can be expressed as [1; 1, 1, 1, 1, ...] in continued fraction form.