RE: Puzzler's Edge
03-06-2017, 02:07 PM
I would probably suggest using something that isn't desmos
Ok let's try something.
You (probably) don't want to graph every single rational number, desmos will not be happy with you if you try to do that.
However, if you're willing to settle for some loss of quality, you can consider all fractions of form 1/N, 2/N, 3/N, etc. with the following:
N/gcd(mod(floor(N*x),N),N) = D
This extracts the denominator. The fraction itself can be extracted from floor(N*x)/N = F. Thus you can extract the numerator N = F*D.
You probably want to set N to some highly factorable number like 30 or 60 or 120 or 210 or something. (You'll quickly see that setting N to too large of a number will not make desmos happy, which is why over the reals (or a floating point approximation as desmos uses) this isn't very feasible)
If you're doing stuff to the fractions, you'll probably have do manual rational arithmetic to get your desired results. Like A/B+C/D = (AD+BC)/BD and the like. But since you have the numerators and denominators of both in simplest form this should not be too bad.
Ok let's try something.
You (probably) don't want to graph every single rational number, desmos will not be happy with you if you try to do that.
However, if you're willing to settle for some loss of quality, you can consider all fractions of form 1/N, 2/N, 3/N, etc. with the following:
N/gcd(mod(floor(N*x),N),N) = D
This extracts the denominator. The fraction itself can be extracted from floor(N*x)/N = F. Thus you can extract the numerator N = F*D.
You probably want to set N to some highly factorable number like 30 or 60 or 120 or 210 or something. (You'll quickly see that setting N to too large of a number will not make desmos happy, which is why over the reals (or a floating point approximation as desmos uses) this isn't very feasible)
If you're doing stuff to the fractions, you'll probably have do manual rational arithmetic to get your desired results. Like A/B+C/D = (AD+BC)/BD and the like. But since you have the numerators and denominators of both in simplest form this should not be too bad.