zju 2370 Expanding Rods【解题报告】

Expanding Rods

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Time limit: 1 Seconds   Memory limit: 32768K  
Total Submit: 460   Accepted Submit: 128  

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When a thin rod of length L is heated n degrees, it expands to a new length L'=(1+n*C)*L, where C is the coefficient of heat expansion.

When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment.

 

Your task is to compute the distance by which the center of the rod is displaced.

Input

The input contains multiple lines. Each line of input contains three non-negative numbers: the initial lenth of the rod in millimeters, the temperature change in degrees and the coefficient of heat expansion of the material. Input data guarantee that no rod expands by more than one half of its original length. The last line of input contains three negative numbers and it should not be processed.

Output

For each line of input, output one line with the displacement of the center of the rod in millimeters with 3 digits of precision.

Sample Input

1000 100 0.0001
15000 10 0.00006
10 0 0.001
-1 -1 -1

Sample Output

61.329
225.020
0.000

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ps：
    本来这个题目并不难，只要二分一下就可以了。但关键就在于二分什么。可以选择二分答案，也可以选择二分角度，这两种都是我率先尝试的，但都不对。后来看了SHOIT的程序选择了二分半径，就可以过了。
    对于这种几何问题，有的时候是有些难以把握的，按照道理，二分答案应该是最准确的了，但这里如果我二分的是答案，那么在计算上面就要引入atan的调用，带来误差（虽然二分半径也要引入asin）。标称怎么给我们并不知道，碰到问题，还需要多尝试一下才行。