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PLS, HELP! Tricky integers

  1. Nov 20, 2007 #1
    Given 3 equations:

    1) 1/2pi + 2Pi(x) = 3.90625F
    2) pi + 2Pi(y) = 7.65625F
    3) 3/2pi + 2Pi(z) = 11.2500F

    Find such F so that x, y and z are integers; maximum error on the left side can be +- pi/7.

    How would you tackle this one? I am still trial'n'erroring..
  2. jcsd
  3. Nov 21, 2007 #2


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    Science Advisor

    ?? Those are basically just arithmetic problems aren't they? First pi/7 is approximately 0.44880 so that's the accuracy you need- not very accurate at all! Using five decimal place accuracy to start with should be enough. Assuming that by "1/2pi" you mean (1/2)pi and not 1/(2pi), then the first equation becomes 1.57080+ 6.28318x= 3.90625F. Solve for x:
    6.28318x= 3.90625F- 1.57080. Divide by 6.28318: x= .62170F- .25000. Do the same for y and z. It should not be hard to find a value for F so that each of those will be within [itex]pi/7[/itex] of an integer.
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