Given a convex plane region with area 
and perimeter 
,
 |
where 
is the number of enclosed lattice points (Nosarzewska
1948). This improves on Jarnick's inequality
 |
Nosarzewska's Inequality
See also
Jarnick's Inequality, Lattice PointExplore with Wolfram|Alpha
References
Nosarzewska, M. "Évaluation de la différence entre l'aire d'une région plane convexe et le nombre des points aux coordonnées entières couverts par elle." Colloq. Math. 1, 305-311, 1948.Referenced on Wolfram|Alpha
Nosarzewska's InequalityCite this as:
Weisstein, Eric W. "Nosarzewska's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NosarzewskasInequality.html