degrees radians conversion

Hi all,

I'm having a problem where the numeric error in converting between degrees and radians is causing problems.

What I would like to do, is define a set of real numbers X where the conversion from radians to degrees can be inverted exactly, so

(x * (180/pi)) * (pi/180) = x for all x in X

then whenever I get a value in radians I can map it to its closest value in X and problem solved. But I don't know how to do that.

I was thinking I could loop the rads->degs->rads process until it finds an exactly invertible value. I have no idea if this is guaranteed to converge, or if it will converge to a value anywhere near the original.

My other thought was that there might be a property where any x with less than c significant figures will be a member of X.

Thanks for any help,
Andrew
.

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