For ten points, identify this country, home to Bravais, Fourier, and Lagrange.
A mathematician from this country names a special case of the principle of least action stating that physical systems follow the path with the shortest length. A mathematician from this country names lattices generated by discrete translation operators. Another mathematician from this country introduced the adele ring. The equation ax2 + by2 + cz2 = 0 is named for a mathematician from this country, and a di erent mathematician from this country names the standard   measure used for Euclidean space. A mathematician from this country names series used to represent functions as the sums of sine waves. For ten points, identify this country, home to Bravais, Fourier, and Lagrange.
A mathematician from this country names a special case of the principle of least action stating that physical systems follow the path with the shortest length.
France [liberally accept historical names like  Third French Republic ]