[[Image:Euclid's_Orchard.svg|thumb|Plan view of one corner of Euclid's orchard, in which trees are labelled with the x co-ordinate of their projection on the plane x + y = 1 .]] In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from (x, y, 0) to (x, y, 1) , where x and y are positive integers. The trees visible from the origin are those at lattice points (x, y, 0) , where x and y are coprime, i.e., where the fraction x⁄y is in reduced form. The name Euclid's orchard is derived from the Euclidean algorithm. If the orchard is projected relative to the origin onto the plane x + y = 1 (or, equivalently, drawn in perspective from a viewpoint at the origin) the tops of the trees form a graph of Thomae's function. The point (x, y, 1) projects to The solution to the Basel problem can be used to show that the proportion of points in the n\times n grid that have trees on them is approximately and that the error of this approximation goes to zero in the limit as n goes to infinity.