Find Integer Solutions for Tricky Equations with Maximum Error of +- pi/7

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The discussion focuses on solving three equations involving integer solutions for variables x, y, and z, with a maximum error of ±π/7. The equations are: 1) 1/2π + 2π(x) = 3.90625F, 2) π + 2π(y) = 7.65625F, and 3) 3/2π + 2π(z) = 11.2500F. The participants emphasize the need for a precision of five decimal places and suggest that finding an appropriate value for F will yield integer solutions for x, y, and z within the specified error margin.

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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..
 
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?? 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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