 Planes and spheres. These are the counterparts in space of lines and circles in the plane. An equation such as \(z = 3x + 2y\) defines not a straight line but rather a flat plane, in this case the unique plane passing through the points (0, 1, 2), (1, 0, 3), and (1, 1, 5). And the sphere of radius \(r\) centered on the origin is given by \(x^2 +y^2 +z^2 = r^2\). The roots of a polynomial in \(x, y\) and \(z\) form a surface in space called a two-dimensional variety, of degree that of the polynomial, just as for one-dimensional varieties. Thus planes are of degree 1 and spheres of degree 2.