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标题: 近似表达圆周率 [打印本页]

作者: sean9991 时间: 2005-9-19 20:40
标题: 近似表达圆周率

用数字1-9各一次近似表达圆周率，如：3 + (16 - 8^{-5) / (97 + 2⁴⁾}www.ddhw.com运算符号限 +, -, ×, /, 乘方，要求精度比上述例子要高。

作者: ob 时间: 2005-9-20 23:25
标题: 回复：近似表达圆周率

3+(15-8/7)/(96+4/2)=3.1413994

作者: sean9991 时间: 2005-9-20 23:39
标题: 回复：回复：近似表达圆周率

Nice try. Can you beat the accuracy of the example 3+(16-8^(-5))/(97+2^4) = 3.14159265 ?

作者: ob 时间: 2005-9-21 09:15
标题: 回复：回复：回复：近似表达圆周率

3+(1+5-4)*8/(2^7-9-6)=3.14159292

That's the best I can get so far.

作者: sean9991 时间: 2005-9-21 17:49
标题: One way of solving it

First, we have 1 / (Pi - 3) = 7.0625, so we start with 3 + 1 / (7 + 4^(-2)).

Next, (Pi - 3) / (1 / 7.0625) = 0.999998116, so we should try (1 - x) / 7.0625 = Pi - 3.

Third, use the remaining digits 5, 6, 8, 9 to approximate x = 1 - 0.999998116 = 0.000001884.

Since 9^(-6) = 0.000001882, which is a litte smaller, we can adjust it with 9^(8^(-5)-6).

Hence, the final approximation 3 + (1 - 9^(8^(-5)-6)) / (7 + 2^(-4)) = 3.1415926539

作者: ob 时间: 2005-9-21 19:43
标题: [@};-][@};-][@};-]

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