The Gauss Circle Problem: find the number of integer lattice points inside a circle.

My question is: why was Gauss studying this problem? Was it just math for math's sake, or was this a part of a larger problem he wanted to solve?

I'm guessing there must be a connection to Gaussian integers, but I tried to find the origin on math history books and couldn't find anything.


Gauss was motivated by arithmetic. He wanted to study the asymptotic behavior of the number of representations of integers as a sum of two squares (of integers).

See, for example, K. Chandrasekharan, Introduction to analytic number theory, Springer, 1968.


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