Diophantine Approximation: find lowest possible denominator to approximate within given precision
R, Xx bytes
Note: this challenge is quite a good introductory-challenge for R, which is the 'language-of-the-month' for September 2020, so I've blanked-out my answer in the hope of encouraging some other golfers to have a shot at it in R, too...


 50 bytes


    function(x,e,s=1:e^-1)s[(x-round(x*s)/s)^2&lt;e^2][1]

Try it online!
Function with arguments x &amp; error e.  Can handle negative x (even though not required for challenge)

Note 2: dammit!  a port of xnor's approach is 6 bytes shorter still:


 44 bytes


    function(x,e,s=1:e^-1)s[(x+e)%%(1/s)&lt;2*e][1]

Try it online!