A square is inscribed in a circle of radius \(n\). Verify that the ratio of the area of the square to the area of the circle is equal to \(\frac{2}{\pi} \approx 0.637\).
Proof:
Radius of the circle \(=\)
Area of the circle \(=\)
Area of the triangle \(BOC =\)
Total area of the square \(ABCD =\)
\(\frac{A_{\text{Square}}}{A_{\text{Circle}}} =\)
\(=\)
Hence proved.
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