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Home » "Game of Thrones 2025 Is Real—What Secret Alliances Will Shatter the Throne?") - Carbonext

"Game of Thrones 2025 Is Real—What Secret Alliances Will Shatter the Throne?") - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \text{Ratio} = \frac{A_{\text{circle}}}{A_{\text{octagon}}} = \frac{\pi x^2}{2(1 + \sqrt{2})x^2} = \frac{\pi}{2(1 + \sqrt{2})}

📌 Thus, the ratio of the area of the circle to the area of the octagon is \(\boxed{\frac{\pi}{2(1 + \sqrt{2})}}\).

📌 A computer scientist is designing an AI interface that uses equilateral triangular logic gates. Each gate has a side length of \( s \). If the side length is increased by 50%, what is the ratio of the new area to the original area of one triangular gate?

📌 To find the ratio of the new area to the original area after increasing the side length, we calculate the areas before and after the change.

📌 Original Triangular Area:

📌 The area \( A \) of an equilateral triangle with side \( s \) is given by:

📌 A_{\text{original}} = \frac{\sqrt{3}}{4}s^2

📌 New Triangular Area:

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