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📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 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:

📌 The side length is increased by 50%, so the new side length is \( 1.5s \). The new area is:

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Next, find absolute deviations: |0.8−1.0| = 0.2, |1.2−1.0| = 0.2, |1.5...
Sum of absolute deviations: 0.2 + 0.2 + 0.5 + 0.1 + 0.6 = <<0.2+0.2+0....
Mean absolute deviation: 1.6 / 5 = <<1.6/5=0.32>>0.32
#### 0.32
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