 Algebraic geometry begins with what we referred to in the introduction as shapes, for example lines \(y = ax +b\), circles \(x^2 +y^2 = r^2\), spheres \(x^2 +y^2 +z^2 = r^2\), conic sections \(f(x, y) = 0\) where \(f\) is a quadratic polynomial in \(x\) and \(y\), quadric surfaces \(f(x, y, z) = 0\) with \(f\) again quadratic, and so on.