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Home » \(b_8 = 34 + 21 = 55\) - Esdistancia

\(b_8 = 34 + 21 = 55\) - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 What is the smallest number of whole non-overlapping circles with radius 1 needed to cover a square with side length 4 exactly?

📌 To solve this problem, we first consider the area of the square and the circles. The area of the square with side length 4 is given by:

📌 A_{\text{square}} = 4^2 = 16

📌 The area of one circle with radius 1 is:

📌 A_{\text{circle}} = \pi \times 1^2 = \pi

📌 To cover the square completely, the total area of the circles must be at least equal to the area of the square. However, due to the geometric arrangement, we also need to consider overlap and arranging the circles.

📌 A circle of radius 1 has a diameter of 2. We can arrange 4 circles in a 2x2 grid pattern, each touching its neighbors, to cover the square. Each circle covers a 2x2 portion, and thus 4 circles will cover the entire 4x4 square without leaving any uncovered areas.

📌 Thus, the smallest number of whole non-overlapping circles needed is:

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