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Problem 476

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Circle Packing II

Let R(a, b, c) be the maximum area covered by three non-overlapping circles inside a triangle with edge lengths a, b and c.

Let S(n) be the average value of R(a, b, c) over all integer triplets (a, b, c) such that 1 ≤ a ≤ b ≤ c < a + b ≤ n

You are given S(2) = R(1, 1, 1) ≈ 0.31998, S(5) ≈ 1.25899.

Find S(1803) rounded to 5 decimal places behind the decimal point.

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圆圈打包II

记R(a, b, c)是三边长分别为a，b，c的三角形内部三个互不重叠的圆覆盖的最大面积。

对于所有满足1 ≤ a ≤ b ≤ c < a + b ≤ n的整数三元组(a, b, c)，记S(n)为所有R(a, b, c)的平均值。

已知S(2) = R(1, 1, 1) ≈ 0.31998，S(5) ≈ 1.25899。

求S(1803)并保留小数点后5位小数。

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