The golden ratio, often denoted by the Greek letter \(\phi\) (phi), is defined as:

\[
\phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887
\]

The inverse of the golden ratio is simply the reciprocal of \(\phi\), which can be calculated as:

\[
\frac{1}{\phi} = \frac{2}{1 + \sqrt{5}}
\]

Simplifying this expression, you get:

\[
\frac{1}{\phi} = \phi - 1 \approx 0.6180339887
\]

So, the inverse of the golden ratio is approximately \(0.6180339887\).

Would you like more details or have any questions? Here are some related questions:

1. How is the golden ratio derived?
2. What are the properties of the golden ratio?
3. How is the golden ratio used in mathematics and art?
4. Can the golden ratio be represented as a continued fraction?
5. What is the relationship between the golden ratio and Fibonacci numbers?

**Tip:** The golden ratio appears frequently in nature, art, and architecture, making it a fascinating topic to explore beyond mathematics!

Explore the mathematical concept of the golden ratio and learn how to calculate its inverse. This detailed guide covers the relevant algebraic formulas and properties, making it ideal for students in Grades 10-12.

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