Given a convex plane region with area  and perimeter 
, then
where 
 is the number of enclosed lattice points.
 
	    
	
    
Given a convex plane region with area  and perimeter 
, then
where 
 is the number of enclosed lattice points.
Weisstein, Eric W. "Jarnick's Inequality." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JarnicksInequality.html