Gauss's Circle Problem

​
r
5.
N(r) = π
2
r
+0.492037r
Count the number of lattice points
N(r)
inside the boundary of a circle of radius
r
with center at the origin. Then
N(r)
can be written
N(r)π
2
r
+E(r)
, where Gauss showed that
E(r)≤2
2
πr≈8.8858r
.

External Links

Gauss Circle Problem (Wolfram MathWorld)

Permanent Citation

Eric W. Weisstein
​
​"Gauss's Circle Problem"​
​http://demonstrations.wolfram.com/GausssCircleProblem/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007