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楼主 |
发表于 2025-1-4 16:50:00
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4边=整数的梯形, 整数面积S可以是这些数。
{S -> 9, S -> 10, S -> 12, S -> 14, S -> 15, S -> 16, S -> 18, S -> 20, S -> 22, S -> 24, S -> 26, S -> 30, S -> 32, S -> 35, S -> 36, S -> 40, S -> 42, S -> 45, S -> 48, S -> 50, S -> 54, S -> 55, S -> 56, S -> 60, S -> 63,
S -> 64, S -> 65, S -> 66, S -> 72, S -> 78, S -> 80, S -> 81, S -> 84, S -> 88, S -> 90, S -> 96, S -> 99, S -> 102, S -> 104, S -> 108, S -> 112, S -> 114, S -> 117, S -> 120, S -> 126, S -> 132, S -> 135, S -> 138,
S -> 140, S -> 144, S -> 150, S -> 153, S -> 156, S -> 162, S -> 168, S -> 174, S -> 180, S -> 186, S -> 192, S -> 196, S -> 198, S -> 204,S -> 210, S -> 216, S -> 222, S -> 228, S -> 234, S -> 240, S -> 246, S -> 252}
Union@Flatten@Table[Solve[{((d + a) Sqrt[((d - a + c)^2 - b^2) (b^2 - (d - a - c)^2)])/(4 (d - a)) == S, c - b < d - a < c + b}, {S}, Integers], {n,16,16}, {a, n}, {b, n}, {c, b, n}, {d, a + 1, c + b - 1}] |
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