Perhaps the best way to view the plane is via linear algebra. Using the standard construction via homogeneous coordinates, we can identify the points with the non-zero ordered triples of binary digits, excluding 000. This can be done in such a way that for every two points we can find the third point on the line through the two by adding modulo 2 in each position. In other words, the points of the Fano plane correspond to the non-zero points of the finite vector space F23 of dimension 3 over F2 , the finite field of order 2. A line in the Fano plane corresponds to a 2-dimensional subspace of F23: the points a, b, c are collinear if and only if a + b = c (equivalently, b + c = a, or c + a = b).